A110451 a(n) = n*(4*n^2 + 2*n + 1).

0, 7, 42, 129, 292, 555, 942, 1477, 2184, 3087, 4210, 5577, 7212, 9139, 11382, 13965, 16912, 20247, 23994, 28177, 32820, 37947, 43582, 49749, 56472, 63775, 71682, 80217, 89404, 99267, 109830, 121117, 133152, 145959, 159562, 173985, 189252

Offset: 0

Author

Reinhard Zumkeller, Jul 21 2005

Keywords

• nonn
• easy

Comments

a(n) = A110449(2*n,n), central terms in triangle A110449.

2*a(n) is the sum of the consecutive integers from A000384(n)+1 to A000384(n+1)-1. - Bruno Berselli, Jun 27 2018

Links

• G. C. Greubel, Table of n, a(n) for n = 0..5000
• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Crossrefs

Cf. A000384, A110449.

Programs

GAP

List([0..40],n->n*(4*n^2+2*n+1)); # Muniru A Asiru, Jun 27 2018

Magma

[n*(4*n^2+2*n+1): n in [0..40]]; // Vincenzo Librandi, Dec 26 2010

Maple

seq(n*(4*n^2+2*n+1),n=0..40); # Muniru A Asiru, Jun 27 2018

Mathematica

Table[n*(4*n^2 + 2*n + 1), {n, 0, 50}] (* or *) LinearRecurrence[{4,-6,4,-1}, {0,7,42,129}, 50] (* G. C. Greubel, Aug 24 2017 *)

PARI

x='x+O('x^50); Vec((7*x + 14*x^2 + 3*x^3)/(1 - x)^4) \\ G. C. Greubel, Aug 24 2017

Formula

From G. C. Greubel, Aug 24 2017: (Start)

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

G.f.: (7*x + 14*x^2 + 3*x^3)/(1 - x)^4.

E.g.f.: x*(7 + 14*x + 4*x^2)*exp(x). (End)