A220425 a(n) = n^2 + 2*n + 2^n.

1, 5, 12, 23, 40, 67, 112, 191, 336, 611, 1144, 2191, 4264, 8387, 16608, 33023, 65824, 131395, 262504, 524687, 1049016, 2097635, 4194832, 8389183, 16777840, 33555107, 67109592, 134218511, 268436296, 536871811, 1073742784, 2147484671, 4294968384, 8589935747

Offset: 0

Author

Dario Piazzalunga, Dec 14 2012

Keywords

• nonn
• easy

Links

• Iain Fox, Table of n, a(n) for n = 0..3321
• Index entries for linear recurrences with constant coefficients, signature (5,-9,7,-2).

Programs

Mathematica

Table[n^2 + 2*n + 2^n, {n, 0, 50}] (* T. D. Noe, Dec 14 2012 *)

Maxima

makelist(n^2+2*n+2^n, n, 0, 20); /* Martin Ettl, Dec 15 2012 */

PARI

a(n)=n^2+2*n+2^n \\ Charles R Greathouse IV, Oct 07 2015

PARI

first(n) = Vec((1 - 4*x^2 + x^3)/((1 - x)^3 * (1 - 2*x)) + O(x^n)) \\ Iain Fox, Aug 08 2018

Formula

G.f.: (x^3-4*x^2+1) / ((x-1)^3*(2*x-1)). - Colin Barker, May 09 2013

E.g.f.: exp(x) * (exp(x) + x*(3 + x)). - Iain Fox, Aug 08 2018