A083580 Binomial transform of A083579.

0, 1, 3, 10, 34, 114, 374, 1202, 3798, 11842, 36550, 111954, 340982, 1034210, 3127206, 9434866, 28419286, 85503618, 257035142, 772219538, 2319017910, 6962034466, 20896589158, 62711787570, 188181500054, 564640969154

Offset: 0

Author

Paul Barry, May 01 2003

Keywords

• easy
• nonn

Examples

			a(0) = 2/3-5/12-1/4 = 0 (use 0^0=1).
		

Links

• Index entries for linear recurrences with constant coefficients, signature (7,-16,12).

Crossrefs

Cf. A083579.

Programs

Mathematica

CoefficientList[Series[x*(1 - 4*x + 5*x^2)/((1 - 2*x)^2*(1 - 3*x)), {x, 0, 30}], x] (* Wesley Ivan Hurt, Dec 28 2023 *)

Formula

a(n) = 2*3^n/3-5*0^n/12-(n+1)*2^(n-2).

G.f.: x*(1-4*x+5*x^2)/((1-2*x)^2*(1-3*x)). - Colin Barker, Apr 16 2012