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

1,4

Links

Table of n, a(n) for n=1..35.

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

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)).

Example

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

Mathematica

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

Prog

(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

Crossrefs

Sequence in context: A132979 A163314 A018183 * A367217 A200662 A371792

Adjacent sequences: A196784 A196785 A196786 * A196788 A196789 A196790

Keyword

nonn,easy

Author

Aditya Subramanian, Oct 06 2011

Extensions

Better name from Charles R Greathouse IV, Oct 06 2011

Edited and corrected by Georg Fischer, Apr 03 2019

Status

approved