The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A111647 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A111647

a(n) = A001541(n)*A001653(n+1)*A002315(n).
(history; published version)

#18 by Ray Chandler at Mon Feb 05 12:45:18 EST 2024

STATUS

editing

approved

#17 by Ray Chandler at Mon Feb 05 12:44:01 EST 2024

NAME

a(n) = A001541(n)*A001653(n+1)*A002315(n).

STATUS

approved

editing

Discussion

Mon Feb 05

12:45

Ray Chandler: Correct name/formula to agree with offset of A001653.

#16 by R. J. Mathar at Wed Jan 31 05:42:10 EST 2024

STATUS

editing

approved

#15 by R. J. Mathar at Wed Jan 31 05:41:44 EST 2024

LINKS

<a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (204,-1190,204,-1).

FORMULA

2*a(n) = A001109(n+1) + A097731(n) + 6*A097731(n-1). - R. J. Mathar, Jan 31 2024

KEYWORD

nonn,easy

STATUS

approved

editing

#14 by Charles R Greathouse IV at Thu Sep 08 08:45:21 EDT 2022

PROG

(MAGMAMagma) m:=30; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((1+3*x^3-17*x^2-99*x)/((x^2-6*x+1)*(x^2-198*x+1)))); // G. C. Greubel, Jul 15 2018

Discussion

Thu Sep 08

08:45

OEIS Server: https://oeis.org/edit/global/2944

#13 by Susanna Cuyler at Sun Jul 15 22:10:11 EDT 2018

STATUS

proposed

approved

#12 by G. C. Greubel at Sun Jul 15 17:23:55 EDT 2018

STATUS

editing

proposed

#11 by G. C. Greubel at Sun Jul 15 17:23:19 EDT 2018

LINKS

G. C. Greubel, <a href="/A111647/b111647.txt">Table of n, a(n) for n = 0..434</a>

FORMULA

2*a(n) = A001109(3n3*n+1) + A001109(n+1); e.g., 2*99*169*239 = 7997214+204.

a(n) = sqrt(A011900(2n2*n)*A046090(2n2*n)*A001109(2n2*n+1)); e.g., 20213 = sqrt(493*697*1189).

a(n) = A001541(3n3*n) + 2*A001109(n)*A001541(n-1)*A001541(n); e.g., 105=99+2*1*1*3; 3998709=3880899+2*35*17*99.

For n>0, a(n) = A001652(3n3*n) - A053141(2n2*n)*A002315(n-1) - A001652(n-1); e.g., 105=119-14*1-0; 3998709=4684659-16730*41-20.

G.f.: (1+3*x^3-17*x^2-99*x)/((x^2-6*x+1)*(x^2-198*x+1)). [- Maksym Voznyy (voznyy(AT)mail.ru), Jul 27 2009]

MATHEMATICA

CoefficientList[Series[(1+3*x^3-17*x^2-99*x)/((x^2-6*x+1)*(x^2-198*x+1)), {x, 0, 30}], x] (* G. C. Greubel, Jul 15 2018 *)

PROG

(PARI) x='x+O('x^30); Vec((1+3*x^3-17*x^2-99*x)/((x^2-6*x+1)*(x^2-198*x+1))) \\ G. C. Greubel, Jul 15 2018

(MAGMA) m:=30; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((1+3*x^3-17*x^2-99*x)/((x^2-6*x+1)*(x^2-198*x+1)))); // G. C. Greubel, Jul 15 2018

STATUS

approved

editing

#10 by Alois P. Heinz at Mon Feb 05 15:01:33 EST 2018

STATUS

proposed

approved

#9 by Andrew Howroyd at Mon Feb 05 14:57:30 EST 2018

STATUS

editing

proposed