A158498 a(n) = (1/2)*(n^3 - 6*n^2 + 13*n - 6).

1, 2, 3, 7, 17, 36, 67, 113, 177, 262, 371, 507, 673, 872, 1107, 1381, 1697, 2058, 2467, 2927, 3441, 4012, 4643, 5337, 6097, 6926, 7827, 8803, 9857, 10992, 12211, 13517, 14913, 16402, 17987, 19671, 21457, 23348, 25347, 27457, 29681

Offset

1,2

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Formula

a(n) = (1/2)*(n^3 - 6*n^2 + 13*n - 6).

G.f.: x*(1 - 2*x + x^2 + 3*x^3) / (1-x)^4.

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). - G. C. Greubel, Feb 19 2017

Mathematica

Table[(1/2)*(n^3 - 6*n^2 + 13*n - 6), {n, 1, 50}] (* or *) LinearRecurrence[{4, -6, 4, -1}, {1, 2, 3, 7}, 50] (* G. C. Greubel, Feb 19 2017 *)

Prog

(PARI) x='x+O('x^50); Vec(x*(1 - 2*x + x^2 + 3*x^3) / (1-x)^4) \\ G. C. Greubel, Feb 19 2017
(PARI) a(n)=(n^3 - 6*n^2 + 13*n - 6)/2 \\ Charles R Greathouse IV, Feb 19 2017

Crossrefs

Sequence in context: A030086 A078721 A077007 * A267601 A155548 A191033

Adjacent sequences: A158495 A158496 A158497 * A158499 A158500 A158501

Keyword

nonn,easy

Author

Alexander R. Povolotsky, Jan 13 2011

Status

approved