The On-Line Encyclopedia of Integer Sequences (OEIS)

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A376731

Expansion of (1 - x^4 - x^5)/((1 - x^4 - x^5)^2 - 4*x^9).
(history; published version)

#10 by Michael De Vlieger at Thu Oct 03 09:57:08 EDT 2024

STATUS

proposed

approved

#9 by Seiichi Manyama at Thu Oct 03 08:39:19 EDT 2024

STATUS

editing

proposed

#8 by Seiichi Manyama at Thu Oct 03 03:36:00 EDT 2024

LINKS

<a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,2,2,0,0,-1,2,-1).

FORMULA

a(n) = 2*a(n-4) + 2*a(n-5) - a(n-8) + 2*a(n-9) - a(n-10).

CROSSREFS

Cf. A376725, A376728.

#7 by Seiichi Manyama at Thu Oct 03 01:36:10 EDT 2024

PROG

(PARI) my(N=60, x='x+O('x^N)); Vec((1-x^4-x^5)/((1-x^4-x^5)^2-4*x^9))

#6 by Seiichi Manyama at Thu Oct 03 01:01:33 EDT 2024

FORMULA

a(n) = Sum_{k=0..floor(n/4)} binomial(2*k,2*n-8*k).

#5 by Seiichi Manyama at Thu Oct 03 01:00:26 EDT 2024

CROSSREFS

Cf. A376728.

#4 by Seiichi Manyama at Thu Oct 03 00:57:36 EDT 2024

DATA

1, 0, 0, 0, 1, 1, 0, 0, 1, 6, 1, 0, 1, 15, 15, 1, 1, 28, 70, 28, 2, 45, 210, 210, 46, 67, 495, 924, 496, 157, 1002, 3003, 3004, 1121, 1911, 8009, 12871, 8161, 4880, 18684, 43760, 43948, 23409, 41820, 126124, 184988, 133285, 113373, 324616, 647112, 657273, 454366

PROG

(PARI) a(n) = sum(k=0, n\4, binomial(2*k, 2*n-8*k));

#3 by Seiichi Manyama at Thu Oct 03 00:54:12 EDT 2024

CROSSREFS

Cf. A108479, A376729, A376730.

#2 by Seiichi Manyama at Thu Oct 03 00:52:54 EDT 2024

NAME

allocated for Seiichi Manyama

Expansion of (1 - x^4 - x^5)/((1 - x^4 - x^5)^2 - 4*x^9).

DATA

1, 0, 0, 0, 1, 1, 0, 0, 1, 6, 1, 0, 1, 15, 15, 1, 1, 28, 70, 28, 2, 45, 210, 210, 46, 67, 495, 924, 496, 157, 1002, 3003

OFFSET

0,10

KEYWORD

allocated

nonn

AUTHOR

Seiichi Manyama, Oct 03 2024

STATUS

approved

editing

#1 by Seiichi Manyama at Thu Oct 03 00:52:54 EDT 2024

NAME

allocated for Seiichi Manyama

KEYWORD

allocated

STATUS

approved