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

0,2

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).

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)

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 *)

Prog

(Magma)[n*(4*n^2+2*n+1): n in [0..40]]; // Vincenzo Librandi, Dec 26 2010
(PARI) x='x+O('x^50); Vec((7*x + 14*x^2 + 3*x^3)/(1 - x)^4) \\ G. C. Greubel, Aug 24 2017
(GAP) List([0..40], n->n*(4*n^2+2*n+1)); # Muniru A Asiru, Jun 27 2018

Crossrefs

Cf. A000384, A110449.

Sequence in context: A297405 A044109 A195320 * A212144 A266387 A008526

Adjacent sequences: A110448 A110449 A110450 * A110452 A110453 A110454

Keyword

nonn,easy

Author

Reinhard Zumkeller, Jul 21 2005

Status

approved