A364591 -id:A364591 - cp's OEIS frontend

A364590 G.f. satisfies A(x) = 1/(1-x) + x^4*A(x)^3.

1, 1, 1, 1, 2, 4, 7, 11, 19, 37, 74, 142, 268, 518, 1033, 2077, 4152, 8290, 16687, 33899, 69148, 141160, 288650, 592354, 1220086, 2519226, 5210164, 10794088, 22408556, 46613554, 97125751, 202662419, 423459427, 886048249, 1856448852, 3894362560, 8178530890

Offset: 0

Seiichi Manyama, Jul 29 2023

Cf. A346073, A364591.

Cf. A049130, A199475, A364589.

a(n) = sum(k=0, n\4, binomial(n-2*k, 2*k)*binomial(3*k, k)/(2*k+1));

a(n) = Sum_{k=0..floor(n/4)} binomial(n-2*k,2*k) * binomial(3*k,k) / (2*k+1).

A364588 G.f. satisfies A(x) = 1/(1-x) + x^2*A(x)^4.

Original entry on oeis.org

1, 1, 2, 5, 15, 49, 170, 613, 2275, 8629, 33301, 130333, 516077, 2063685, 8321892, 33803161, 138181521, 568031297, 2346668400, 9737766513, 40569611691, 169632827345, 711611670532, 2994165070045, 12632782541053, 53433933353885, 226540298098019

Offset: 0

Seiichi Manyama, Jul 29 2023

Cf. A049130, A090344.

Cf. A226974, A349289, A364591.

a(n) = sum(k=0, n\2, binomial(n+k, 3*k)*binomial(4*k,k)/(3*k+1));

a(n) = Sum_{k=0..floor(n/2)} binomial(n+k,3*k) * binomial(4*k,k) / (3*k+1).

A369693 G.f. satisfies A(x) = 1/(1-x)^4 + x^4*A(x)^4.

Original entry on oeis.org

1, 4, 10, 20, 36, 72, 220, 936, 4045, 15836, 56174, 187148, 616651, 2114448, 7717752, 29498000, 114243269, 437915876, 1650264874, 6149423732, 22909545269, 86129798600, 327872238092, 1260466647944, 4867739842821, 18801022899756, 72501445905366

Offset: 0

Seiichi Manyama, Jan 29 2024

nonn

Cf. A086615, A369691.

Cf. A364591.

a(n) = sum(k=0, n\4, binomial(n+8*k+3, n-4*k)*binomial(4*k, k)/(3*k+1));

a(n) = Sum_{k=0..floor(n/4)} binomial(n+8*k+3,n-4*k) * binomial(4*k,k) / (3*k+1).

cp's OEIS Frontend

A364590 G.f. satisfies A(x) = 1/(1-x) + x^4*A(x)^3.

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A364588 G.f. satisfies A(x) = 1/(1-x) + x^2*A(x)^4.

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Author

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PARI

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A369693 G.f. satisfies A(x) = 1/(1-x)^4 + x^4*A(x)^4.

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Author

Keywords

Crossrefs

Programs

PARI

Formula