A387647 -id:A387647 - cp's OEIS frontend

A387648 a(n) = Sum_{k=0..floor(n/3)} 2^(n-3k) binomial(2k,2n-6*k).

1, 0, 0, 1, 2, 0, 1, 12, 4, 1, 30, 60, 9, 56, 280, 225, 106, 840, 1681, 852, 2012, 7393, 8102, 6116, 24089, 48288, 39312, 69889, 206354, 268496, 264993, 715868, 1419892, 1498177, 2407662, 5980620, 8659497, 10078152, 21975496, 42559393, 52699770, 81920920, 178653105

Offset: 0

Seiichi Manyama, Sep 04 2025

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

Cf. A108480, A387647.

a(n) = sum(k=0, n\3, 2^(n-3*k)*binomial(2*k, 2*n-6*k));

G.f.: (1-x^3-2*x^4)/((1-x^3-2*x^4)^2 - 8*x^7).

a(n) = 2*a(n-3) + 4*a(n-4) - a(n-6) + 4*a(n-7) - 4*a(n-8).

A387649 a(n) = Sum_{k=0..floor(n/2)} 2^(n-2k) binomial(2k+1,2n-4*k).

Original entry on oeis.org

1, 0, 1, 6, 1, 20, 21, 42, 141, 128, 505, 782, 1465, 3852, 5501, 14290, 26053, 49464, 113313, 195446, 433585, 841732, 1629285, 3477754, 6520445, 13583472, 26955209, 52921182, 109117737, 212250492, 431217101, 861537698, 1706182325, 3460479528, 6839829361

Offset: 0

Seiichi Manyama, Sep 05 2025

Vincenzo Librandi, Table of n, a(n) for n = 0..1500
Index entries for linear recurrences with constant coefficients, signature (0,2,4,-1,4,-4).

Cf. A387624, A387650.

Cf. A387647.

[&+[2^(n-2*k)* Binomial(2*k+1, 2*n-4*k): k in [0..Floor (n/2)]]: n in [0..40]]; // Vincenzo Librandi, Sep 06 2025

Table[Sum[2^(n-2*k)*Binomial[2*k+1,2*n-4*k],{k,0,Floor[n/2]}],{n,0,40}] (* Vincenzo Librandi, Sep 06 2025 *)

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

G.f.: (1-x^2+2*x^3)/((1-x^2+2*x^3)^2 - 8*x^3).

a(n) = 2*a(n-2) + 4*a(n-3) - a(n-4) + 4*a(n-5) - 4*a(n-6).

A387651 a(n) = Sum_{k=0..floor(n/2)} 2^(n-2k) binomial(2k+1,2n-4*k+1).

Original entry on oeis.org

1, 0, 3, 2, 5, 20, 11, 70, 93, 176, 515, 618, 1877, 3212, 6043, 14670, 23469, 55336, 104915, 201202, 442213, 801924, 1711787, 3369814, 6574205, 13748896, 26354723, 54064250, 107762933, 212616060, 434126907, 852642910, 1721793229, 3443972120, 6839443699, 13808517634

Offset: 0

Seiichi Manyama, Sep 05 2025

Vincenzo Librandi, Table of n, a(n) for n = 0..1500
Index entries for linear recurrences with constant coefficients, signature (0,2,4,-1,4,-4).

Cf. A387627, A387652.

Cf. A387647, A387649.

[&+[2^(n-2*k)* Binomial(2*k+1, 2*n-4*k+1): k in [0..Floor (n/2)]]: n in [0..40]]; // Vincenzo Librandi, Sep 05 2025

Table[Sum[2^(n-2*k)*Binomial[2*k+1,2*n-4*k+1],{k,0,Floor[n/2]}],{n,0,40}] (* Vincenzo Librandi, Sep 05 2025 *)

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

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

a(n) = 2*a(n-2) + 4*a(n-3) - a(n-4) + 4*a(n-5) - 4*a(n-6).

cp's OEIS Frontend

A387648 a(n) = Sum_{k=0..floor(n/3)} 2^(n-3k) binomial(2k,2n-6*k).

Views

Author

Keywords

Links

Crossrefs

Programs

PARI

Formula

A387649 a(n) = Sum_{k=0..floor(n/2)} 2^(n-2k) binomial(2k+1,2n-4*k).

Views

Author

Keywords

Links

Crossrefs

Programs

Magma

Mathematica

PARI

Formula

A387651 a(n) = Sum_{k=0..floor(n/2)} 2^(n-2k) binomial(2k+1,2n-4*k+1).

Views

Author

Keywords

Links

Crossrefs

Programs

Magma

Mathematica

PARI

Formula

cp's OEIS Frontend

A387648 a(n) = Sum_{k=0..floor(n/3)} 2^(n-3*k) * binomial(2*k,2*n-6*k).

Views

Author

Keywords

Links

Crossrefs

Programs

PARI

Formula

A387649 a(n) = Sum_{k=0..floor(n/2)} 2^(n-2*k) * binomial(2*k+1,2*n-4*k).

Views

Author

Keywords

Links

Crossrefs

Programs

Magma

Mathematica

PARI

Formula

A387651 a(n) = Sum_{k=0..floor(n/2)} 2^(n-2*k) * binomial(2*k+1,2*n-4*k+1).

Views

Author

Keywords

Links

Crossrefs

Programs

Magma

Mathematica

PARI

Formula

A387648 a(n) = Sum_{k=0..floor(n/3)} 2^(n-3k) binomial(2k,2n-6*k).

A387649 a(n) = Sum_{k=0..floor(n/2)} 2^(n-2k) binomial(2k+1,2n-4*k).

A387651 a(n) = Sum_{k=0..floor(n/2)} 2^(n-2k) binomial(2k+1,2n-4*k+1).