A375282 -id:A375282 - cp's OEIS frontend

A375283 Expansion of 1/((1 - x - x^4)^2 - 4*x^5).

1, 2, 3, 4, 7, 16, 35, 68, 122, 220, 417, 816, 1588, 3028, 5707, 10784, 20547, 39322, 75150, 143144, 272212, 517990, 987005, 1881824, 3586808, 6832874, 13013780, 24789200, 47229672, 89991518, 171459667, 326651952, 622295173, 1185547900, 2258689217, 4303264572

Offset: 0

Seiichi Manyama, Aug 09 2024

nonn

Index entries for linear recurrences with constant coefficients, signature (2,-1,0,2,2,0,0,-1).

Cf. A182890, A375278, A375285.

Cf. A246883, A375282.

my(N=40, x='x+O('x^N)); Vec(1/((1-x-x^4)^2-4*x^5))

a(n) = sum(k=0, n\4, binomial(2*n-6*k+2, 2*k+1))/2;

a(n) = 2*a(n-1) - a(n-2) + 2*a(n-4) + 2*a(n-5) - a(n-8).

a(n) = (1/2) * Sum_{k=0..floor(n/4)} binomial(2*n-6*k+2,2*k+1).

A375284 Expansion of (1 - x - x^5)/((1 - x - x^5)^2 - 4*x^6).

Original entry on oeis.org

1, 1, 1, 1, 1, 2, 7, 16, 29, 46, 68, 107, 191, 364, 686, 1234, 2125, 3596, 6148, 10754, 19132, 34121, 60361, 105725, 184207, 321227, 562628, 989397, 1742190, 3064093, 5377732, 9424960, 16515877, 28964243, 50840968, 89280116, 156762020, 275136201, 482728432

Offset: 0

Seiichi Manyama, Aug 09 2024

nonn

Seiichi Manyama, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (2,-1,0,0,2,2,0,0,0,-1).

Cf. A108479, A375279, A375282.

my(N=40, x='x+O('x^N)); Vec((1-x-x^5)/((1-x-x^5)^2-4*x^6))

a(n) = sum(k=0, n\5, binomial(2*n-8*k, 2*k));

a(n) = 2*a(n-1) - a(n-2) + 2*a(n-5) + 2*a(n-6) - a(n-10).

a(n) = Sum_{k=0..floor(n/5)} binomial(2*n-8*k,2*k).

A376786 Expansion of (1 + x - x^4)/((1 + x - x^4)^2 - 4*x).

Original entry on oeis.org

1, 3, 5, 7, 10, 21, 48, 99, 183, 326, 602, 1165, 2282, 4396, 8318, 15675, 29743, 56841, 108765, 207510, 394809, 750880, 1429845, 2725685, 5196420, 9901692, 18859649, 35921156, 68432064, 130388316, 248437405, 473322419, 901717453, 1717851555, 3272777450

Offset: 0

Seiichi Manyama, Oct 04 2024

nonn

Index entries for linear recurrences with constant coefficients, signature (2,-1,0,2,2,0,0,-1).

Cf. A099511, A376785.

Cf. A375282, A375283, A376718.

my(N=40, x='x+O('x^N)); Vec((1+x-x^4)/((1+x-x^4)^2-4*x))

a(n) = sum(k=0, n\4, binomial(2*n-6*k+1, 2*k+1));

a(n) = 2*a(n-1) - a(n-2) + 2*a(n-4) + 2*a(n-5) - a(n-8).

a(n) = Sum_{k=0..floor(n/4)} binomial(2*n-6*k+1,2*k+1).

cp's OEIS Frontend

A375283 Expansion of 1/((1 - x - x^4)^2 - 4*x^5).

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A375284 Expansion of (1 - x - x^5)/((1 - x - x^5)^2 - 4*x^6).

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A376786 Expansion of (1 + x - x^4)/((1 + x - x^4)^2 - 4*x).

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