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

Author

N. J. A. Sloane, Nov 20 2004

Keywords

• nonn
• easy

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).

Crossrefs

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

Programs

Magma

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

Mathematica

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

SageMath

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

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)

Extensions

More terms from Hugo Pfoertner, Nov 26 2004