A244762 a(n) = (5*3^n-2*n-1)/4.

1, 3, 10, 32, 99, 301, 908, 2730, 8197, 24599, 73806, 221428, 664295, 1992897, 5978704, 17936126, 53808393, 161425195, 484275602, 1452826824, 4358480491, 13075441493, 39226324500, 117678973522, 353036920589, 1059110761791, 3177332285398, 9531996856220, 28595990568687, 85787971706089, 257363915118296

Offset: 0

Author

Franklin T. Adams-Watters, Jul 06 2014

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (5,-7,3).

Crossrefs

Cf. A060816 (first differences).

Cf. A108765, A164039, A047926, A000340.

Programs

Mathematica

CoefficientList[Series[(1-2*x+2*x^2)/((1-3*x)*(1-x)^2), {x, 0, 30}], x] (* Vaclav Kotesovec, Jul 06 2014 *)

Formula

a(n+1) = 3*a(n) + n.

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

E.g.f.: exp(x)*(5*exp(2*x) - 2*x - 1)/4. - Stefano Spezia, Aug 28 2023