The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A168258 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A168258

Triangle read by rows, A101688 * A000012 as infinite lower triangular matrices.
(history; published version)

#23 by Peter Luschny at Thu Nov 17 04:47:31 EST 2022

STATUS

reviewed

approved

#22 by Michel Marcus at Thu Nov 17 01:11:15 EST 2022

STATUS

proposed

reviewed

#21 by Michel Marcus at Thu Nov 17 01:11:10 EST 2022

STATUS

editing

proposed

#20 by Michel Marcus at Thu Nov 17 01:10:14 EST 2022

PROG

lista(nn) = my(ma=matrix(nn, +1, nn, n, k, T(n, -1, k-1)), mb=matrix(nn, nn, n, k, n>=k)); my(m=ma*mb, list=List()); for (n=1, nn, listput(list, vector(n, k, m[n, k]))); Vec(list); \\ Michel Marcus, Nov 16 2022

STATUS

proposed

editing

Discussion

Thu Nov 17

01:11

Michel Marcus: ok; understood and corrected; thanks

01:11

Michel Marcus: ok for me

#19 by Michel Marcus at Wed Nov 16 02:41:17 EST 2022

STATUS

editing

proposed

Discussion

Wed Nov 16

17:31

Gary W. Adamson: Hi Michel.  No.  The target seq is A101688: First few rows are:
1,..........gets.................. .1.. in  A168258
0,1........................... ..1 ,1  not [2,1] in your above. (Dont' add the zero).
0, 1, 1................. .  .2, 2, 1. correct
0, 0,1,1.............. ..2, 2, 2, 1  It's [1,2,2,2], not [3,3,2,1]
0,0,1,1,1.......... ..3,3,3 ,2, 1 correct
0,0,0,1,1,1...... .3,3,3,3,2, 1 correct
0,0,0,1,1,1,1...4,4,4,4 3,2,1 correct.
Note: When going to the left and encountering a 0, don't add a unit.  Thus,
given [0,1], the result has to be [1,1], not [1,2].. Likewise given [0,0,1,1] starting from the right, we get [1,2,2,2],, not [3,3,2,1] since when coming to an 0, no units are added from the previous term..
Results agree with the matrix approach multiplying A101688 * A000012. using my matrix calculator. 
Shanti, Gary

17:48

Gary W. Adamson: [0,0,1,1] in A101688 gets us [2,2,2 1] since when going to the left and encountering a zero, just keep the previous result. (a 2)..  But no matter. Just get a pgm and plug in the matrices and multiply. You'll get the result submitted.  Thanks again!

#18 by Michel Marcus at Wed Nov 16 02:40:14 EST 2022

PROG

(PARI) T(n, k) = if(binomial(k, n-k)>0, 1, 0); \\ A101688

lista(nn) = my(ma=matrix(nn, nn, n, k, T(n, k)), mb=matrix(nn, nn, n, k, n>=k)); my(m=ma*mb, list=List()); for (n=1, nn, listput(list, vector(n, k, m[n, k]))); Vec(list); \\ Michel Marcus, Nov 16 2022

STATUS

proposed

editing

Discussion

Wed Nov 16

02:41

Michel Marcus: thanks, but I don't get exactly the same data; I get [[1], [2, 1], [2, 2, 1], [3, 3, 2, 1], [3, 3, 3, 2, 1], [4, 4, 4, 3, 2, 1], ....

02:41

Michel Marcus: can someone check with another code ?

#17 by Michel Marcus at Wed Nov 16 02:07:25 EST 2022

STATUS

editing

proposed

#16 by Michel Marcus at Wed Nov 16 02:07:15 EST 2022

COMMENTS

The operation A101688 * A000012 transforms rows of A101688 into sequence terms by taking partial sums from the right of A101688 rows. For example, row 3 of A101688 (0, 0, 1, 1) becomes (2, 2, 2, 1). - _Gary W. Adamson_, Nov 15 2022

Discussion

Wed Nov 16

02:07

Michel Marcus: thanks !!

#15 by Michel Marcus at Wed Nov 16 02:06:26 EST 2022

EXTENSIONS

Name corrected by Gary W. Adamson, Nov 15 2022

STATUS

proposed

editing

#14 by Jon E. Schoenfield at Tue Nov 15 22:08:35 EST 2022

STATUS

editing

proposed