A196787 a(n) = 3*a(n-1) - 2*a(n-2) - a(n-4) + a(n-5) with initial terms 1, 1, 1, 3, 6.

1, 1, 1, 3, 6, 12, 24, 46, 87, 163, 303, 561, 1036, 1910, 3518, 6476, 11917, 21925, 40333, 74191, 136466, 251008, 461684, 849178, 1561891, 2872775, 5283867, 9718557, 17875224, 32877674, 60471482, 111224408, 204573593, 376269513, 692067545

Offset: 1

Author

Aditya Subramanian, Oct 06 2011

Keywords

• nonn
• easy

Examples

			a(7) = (a(6): 12) + (a(5): 6) + (a(4): 3) + (n-4: 3) = 24.
		

Links

• Index entries for linear recurrences with constant coefficients, signature (3,-2,0,-1,1).

Programs

Mathematica

LinearRecurrence[{3, -2, 0, -1, 1}, {1, 1, 1, 3, 6}, 42] (* T. D. Noe, Oct 06 2011 *)

PARI

x='x+O('x^43); Vec(x*(-1+2*x-2*x^3) / ((x-1)^2*(x^3+x^2+x-1))) \\ Georg Fischer, Apr 03 2019

Formula

a(1)=1, a(2)=1, a(3)=1; a(n) = a(n-1) + a(n-2) + a(n-3) + n - 4 for n >= 4.

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

Extensions

Better name from Charles R Greathouse IV, Oct 06 2011

Edited and corrected by Georg Fischer, Apr 03 2019