A204674 a(n) = 4*n^3 + 5*n^2 + 2*n + 1.

1, 12, 57, 160, 345, 636, 1057, 1632, 2385, 3340, 4521, 5952, 7657, 9660, 11985, 14656, 17697, 21132, 24985, 29280, 34041, 39292, 45057, 51360, 58225, 65676, 73737, 82432, 91785, 101820, 112561, 124032, 136257, 149260, 163065, 177696, 193177, 209532, 226785, 244960, 264081

Offset: 0

Author

Reinhard Zumkeller, Jan 18 2012

Keywords

• nonn
• easy

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Crossrefs

Row sums of A033293.

Cf. A054567, A226449.

Programs

Haskell

a204674 n = n * (n * (4 * n + 5) + 2) + 1

Mathematica

LinearRecurrence[{4,-6,4,-1},{1,12,57,160},50] (* or *) CoefficientList[ Series[(1+3x)(1+5x)/(1-x)^4,{x,0,50}],x] (* Harvey P. Dale, Jun 25 2021 *)

PARI

a(n)={ 4*n^3 + 5*n^2 + 2*n + 1 } \\ Andrew Howroyd, Jan 07 2020

Formula

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

G.f.: (1 + 3*x)*(1 + 5*x)/(1 - x)^4. - Andrew Howroyd, Jan 07 2020

E.g.f.: exp(x)*(1 + 11*x + 17*x^2 + 4*x^3). - Elmo R. Oliveira, Aug 08 2025

Extensions

Terms a(26) and beyond from Andrew Howroyd, Jan 07 2020