A180415 a(n) = (n^3 - 3n^2 + 14n - 6)/6.

1, 3, 6, 11, 19, 31, 48, 71, 101, 139, 186, 243, 311, 391, 484, 591, 713, 851, 1006, 1179, 1371, 1583, 1816, 2071, 2349, 2651, 2978, 3331, 3711, 4119, 4556, 5023, 5521, 6051, 6614, 7211, 7843, 8511, 9216, 9959, 10741, 11563, 12426, 13331, 14279, 15271, 16308

Offset: 1

Author

Gary W. Adamson, Sep 02 2010

Keywords

• nonn
• easy

Comments

Binomial transform of 0,1,1,0,bar(1,-1), where bar(..) denotes a periodically repeated sequence.

If the offset is set to 0, this is the binomial transform of the quasi-finite sequence 1,2,1,1,bar(0).

Examples

			Representation as binomial transform: a(4) = 11 = (1, 2, 1, 1) dot (1, 3, 3, 1) = (1 + 6 + 3 + 1).
		

Links

• Paolo P. Lava, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Programs

Mathematica

Table[(n^3-3n^2+14n-6)/6,{n,60}]  (* Harvey P. Dale, Mar 04 2011 *)

Formula

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

Extensions

Sequence extended, nomenclature of variables normalized, g.f. multiplied by x, binomial transforms clarified - R. J. Mathar, Sep 04 2010