A387629 -id:A387629 - cp's OEIS frontend

A387623 a(n) = Sum_{k=0..floor(n/4)} 2^k * binomial(2n-6k,2*k).

1, 1, 1, 1, 3, 13, 31, 57, 95, 193, 463, 1081, 2295, 4609, 9423, 20185, 44071, 94801, 199807, 418921, 885879, 1889889, 4034639, 8573561, 18155399, 38461105, 81665695, 173627401, 368961431, 783201921, 1661811055, 3527298329, 7490519335, 15908549329, 33779968447

Offset: 0

Seiichi Manyama, Sep 03 2025

Index entries for linear recurrences with constant coefficients, signature (2,-1,0,4,4,0,0,-4).

Cf. A001541, A108480, A387622.

Cf. A387626, A387629.

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

G.f.: (1-x-2*x^4)/((1-x-2*x^4)^2 - 8*x^5).

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

A387627 a(n) = Sum_{k=0..floor(n/2)} 2^k * binomial(2n-2k+1,2*k+1).

Original entry on oeis.org

1, 3, 7, 27, 83, 263, 855, 2723, 8731, 27999, 89663, 287355, 920771, 2950263, 9453607, 30291667, 97062123, 311012623, 996563855, 3193247403, 10231988371, 32785923879, 105054547063, 336621829635, 1078623042491, 3456186066623, 11074510391007, 35485583833307

Offset: 0

Seiichi Manyama, Sep 03 2025

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (2,3,4,-4).

Cf. A001653, A387628, A387629.

Cf. A099511.

[&+[2^k* Binomial(2*n-2*k+1, 2*k+1): k in [0..Floor (n/2)]]: n in [0..35]]; // Vincenzo Librandi, Sep 04 2025

Table[Sum[2^k*Binomial[2*n-2*k+1,2*k+1],{k,0,Floor[n/2]}],{n,0,40}] (* Vincenzo Librandi, Sep 04 2025 *)

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

G.f.: (1+x-2*x^2)/((1+x-2*x^2)^2 - 4*x).

a(n) = 2*a(n-1) + 3*a(n-2) + 4*a(n-3) - 4*a(n-4).

A387628 a(n) = Sum_{k=0..floor(n/3)} 2^k * binomial(2n-4k+1,2*k+1).

Original entry on oeis.org

1, 3, 5, 9, 29, 81, 185, 429, 1093, 2785, 6817, 16613, 41181, 102441, 253049, 623693, 1541557, 3814929, 9430545, 23297397, 57577997, 142345721, 351858985, 869614109, 2149341925, 5312698977, 13131636417, 32457015109, 80223121469, 198288112969, 490110342873

Offset: 0

Seiichi Manyama, Sep 03 2025

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (2,-1,4,4,0,-4).

Cf. A001653, A387627, A387629.

[&+[2^k* Binomial(2*n-4*k+1, 2*k+1): k in [0..Floor (n/3)]]: n in [0..35]]; // Vincenzo Librandi, Sep 04 2025

Table[Sum[2^k*Binomial[2*n-4*k+1,2*k+1],{k,0,Floor[n/3]}],{n,0,40}] (* Vincenzo Librandi, Sep 04 2025 *)

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

G.f.: (1+x-2*x^3)/((1+x-2*x^3)^2 - 4*x).

a(n) = 2*a(n-1) - a(n-2) + 4*a(n-3) + 4*a(n-4) - 4*a(n-6).

cp's OEIS Frontend

A387623 a(n) = Sum_{k=0..floor(n/4)} 2^k * binomial(2n-6k,2*k).

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A387627 a(n) = Sum_{k=0..floor(n/2)} 2^k * binomial(2n-2k+1,2*k+1).

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Formula

A387628 a(n) = Sum_{k=0..floor(n/3)} 2^k * binomial(2n-4k+1,2*k+1).

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Author

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Magma

Mathematica

PARI

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cp's OEIS Frontend

A387623 a(n) = Sum_{k=0..floor(n/4)} 2^k * binomial(2*n-6*k,2*k).

Views

Author

Keywords

Links

Crossrefs

Programs

PARI

Formula

A387627 a(n) = Sum_{k=0..floor(n/2)} 2^k * binomial(2*n-2*k+1,2*k+1).

Views

Author

Keywords

Links

Crossrefs

Programs

Magma

Mathematica

PARI

Formula

A387628 a(n) = Sum_{k=0..floor(n/3)} 2^k * binomial(2*n-4*k+1,2*k+1).

Views

Author

Keywords

Links

Crossrefs

Programs

Magma

Mathematica

PARI

Formula

A387623 a(n) = Sum_{k=0..floor(n/4)} 2^k * binomial(2n-6k,2*k).

A387627 a(n) = Sum_{k=0..floor(n/2)} 2^k * binomial(2n-2k+1,2*k+1).

A387628 a(n) = Sum_{k=0..floor(n/3)} 2^k * binomial(2n-4k+1,2*k+1).