A026022 -id:A026022 - cp's OEIS frontend

A027297 a(n) = Sum_{k=0..floor((n-3)/2)} T(n,k) * T(n,k+3), with T given by A026022.

1, 4, 30, 104, 567, 1952, 9453, 32900, 150029, 528956, 2327156, 8303216, 35679835, 128633440, 543723257, 1977821700, 8260172309, 30278441400, 125314192728, 462409521376, 1900445030538, 7053236494784, 28828752666375, 107536008386924, 437602449724101

Offset: 3

Clark Kimberling

nonn

More terms from Sean A. Irvine, Oct 26 2019

A027298 a(n) = Sum_{k=0..m} (k+1) * A026022(n, k), where m=n for n=0,1 and m = floor((n+3)/2) for n >= 2.

Original entry on oeis.org

1, 3, 8, 20, 43, 101, 208, 472, 958, 2126, 4288, 9368, 18835, 40673, 81632, 174704, 350266, 744290, 1491232, 3150424, 6309246, 13265138, 26557408, 55610960, 111311068, 232279836, 464856832, 967155824, 1935314563

Offset: 0

Clark Kimberling

nonn

A027299 a(n) = Sum_{k=0..m} (k+1) * A026022(n, m-k), where m=n for n=0,1 and m = floor((n+3)/2) for n >= 2.

Original entry on oeis.org

1, 3, 8, 20, 32, 79, 128, 312, 512, 1234, 2048, 4888, 8192, 19387, 32768, 76976, 131072, 305902, 524288, 1216536, 2097152, 4840950, 8388608, 19273360, 33554432, 76766564, 134217728, 305877616, 536870912, 1219164499, 2147483648

Offset: 0

Clark Kimberling

nonn

A026032 a(n) = C(3n,n) - C(3n,n-4).

Original entry on oeis.org

1, 3, 15, 84, 494, 2988, 18411, 114950, 724845, 4606095, 29451240, 189264672, 1221417360, 7910510312, 51388786107, 334716829674, 2185180379179, 14294808917025, 93680975707935, 614925987859260, 4042236129950970

Offset: 0

Clark Kimberling

nonn

a(n) = T(3n, n), where T is defined in A026022.

Table[Binomial[3n,n]-Binomial[3n,n-4],{n,0,20}] (* Harvey P. Dale, Dec 14 2012 *)

a(n) = binomial(3*n,n) - binomial(3*n,n-4); \\ Michel Marcus, May 10 2020

G.f.: (2*g-1)*(2*g^2-2*g+1)/((3*g-1)*(g-1)^4) where g*(1-g)^2 = x. - Mark van Hoeij, Nov 09 2011

More terms from Ralf Stephan, Jan 09 2005

A026033 C(4n,n) - C(4n,n-4).

Original entry on oeis.org

1, 4, 28, 220, 1819, 15484, 134320, 1180764, 10482340, 93766288, 843822148, 7631018564, 69291185474, 631334484200, 5769124912320, 52851389067420, 485242722376524, 4463782855666480, 41133265444555120

Offset: 0

Clark Kimberling

nonn

a(n) = T(4n, n), where T is defined in A026022.

G.f.: (g-2)*(2-2*g+g^2)*g^2/(3*g-4) where g = 1+x*g^4 is the g.f. of A002293. - Mark van Hoeij, Nov 11 2011

More terms from Ralf Stephan, Jan 09 2005

cp's OEIS Frontend

A027297 a(n) = Sum_{k=0..floor((n-3)/2)} T(n,k) * T(n,k+3), with T given by A026022.

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Extensions

A027298 a(n) = Sum_{k=0..m} (k+1) * A026022(n, k), where m=n for n=0,1 and m = floor((n+3)/2) for n >= 2.

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A027299 a(n) = Sum_{k=0..m} (k+1) * A026022(n, m-k), where m=n for n=0,1 and m = floor((n+3)/2) for n >= 2.

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Keywords

A026032 a(n) = C(3n,n) - C(3n,n-4).

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Programs

Mathematica

PARI

Formula

Extensions

A026033 C(4n,n) - C(4n,n-4).

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Extensions