A214039 - OEIS

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A214039

a(n) = a(n-1) - floor((a(n-2) + a(n-3))/2), with a(n)=n for n < 3.

0, 1, 2, 2, 1, -1, -2, -2, 0, 2, 3, 2, 0, -2, -3, -2, 1, 4, 5, 3, -1, -5, -6, -3, 3, 8, 8, 3, -5, -10, -9, -1, 9, 14, 10, -1, -13, -17, -10, 5, 19, 22, 10, -10, -26, -26, -8, 18, 35, 30, 4, -28, -45, -33, 4, 43, 58, 35, -15, -61, -71, -33, 33, 85, 85

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,3

COMMENTS

The same sequence, except few initial terms, for 23 of the 27 other seed triples satisfying -1 <= a(0,1,2) <= 1. The four exceptions are {-1,1,0}, {0,0,0}, {0,1,0}, {1,0,0} - all 0's after the seed triple. The sequence starting with {1,-1,0} has ten extra terms, the other 22 variants have between 1 and 9, except {1, 1, -1} which lacks 3 terms.

LINKS

Table of n, a(n) for n=0..64.

MATHEMATICA

RecurrenceTable[{a[0]==0, a[1]==1, a[2]==2, a[n]==a[n-1]-Floor[(a[n-2] + a[n-3])/2]}, a[n], {n, 70}] (* Harvey P. Dale, Dec 03 2012 *)

PROG

(Python)

ppp =0

prpr=1

prev=2

for n in range(65):

cur = prev-(prpr+ppp)//2

print(str(ppp), end=', ')