A100431 Bisection of A002417.

8, 80, 336, 960, 2200, 4368, 7840, 13056, 20520, 30800, 44528, 62400, 85176, 113680, 148800, 191488, 242760, 303696, 375440, 459200, 556248, 667920, 795616, 940800, 1105000, 1289808, 1496880, 1727936, 1984760, 2269200, 2583168, 2928640, 3307656, 3722320

Offset

0,1

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Formula

a(n) = (4/3)*(2*n^4 + 11*n^3 + 22*n^2 + 19*n + 6). - Ralf Stephan, May 15 2007

G.f.: 8*(1 + 5*x + 2*x^2)/(1 - x)^5. - Ilya Gutkovskiy, Feb 24 2017

From G. C. Greubel, Apr 09 2023: (Start)

a(n) = (8/3)*binomial(n+2, 2)*binomial(2*n+3, 2).

a(n) = (8/3)*A000217(n+1)*A014105(n+1).

a(n) = 8*A108678(n).

a(n) = 4*A098077(n+1).

E.g.f.: (4/3)*(6 + 54*x + 69*x^2 + 23*x^3 + 2*x^4)*exp(x). (End)

Mathematica

Table[4*(n+1)^2(n+2)(2n+3)/3, {n, 0, 60}] (* Vladimir Joseph Stephan Orlovsky, Jul 07 2011 *)

Prog

(Magma) [4*(n+1)^2*(n+2)*(2*n+3)/3: n in [0..60]]; // G. C. Greubel, Apr 09 2023
(SageMath) [4*(n+1)^2*(n+2)*(2*n+3)/3 for n in range(61)] # G. C. Greubel, Apr 09 2023

Crossrefs

Cf. A000217, A002417, A014105, A098077, A108678.

Sequence in context: A188149 A164755 A050799 * A173116 A102698 A190019

Adjacent sequences: A100428 A100429 A100430 * A100432 A100433 A100434

Keyword

nonn,easy

Author

N. J. A. Sloane, Nov 20 2004

Extensions

More terms from Hugo Pfoertner, Nov 26 2004

Status

approved