A103143 a(n) = a(n-1) + a(n-2) + 3*a(n-3), with a(0) = 1, a(1) = 0, a(2) = 1.

0, 0, 1, 1, 2, 6, 11, 23, 52, 108, 229, 493, 1046, 2226, 4751, 10115, 21544, 45912, 97801, 208345, 443882, 945630, 2014547, 4291823, 9143260, 19478724, 41497453, 88405957, 188339582, 401237898, 854795351, 1821051995, 3879561040, 8264999088, 17607716113

Offset: 0

Author

Paul Barry, Jan 24 2005

Keywords

• easy
• nonn

Comments

Diagonal sums of the Pascal-(1,3,1) triangle A081578.

Links

• R. J. Mathar, Tilings of rectangular regions by rectangular tiles: Counts derived from transfer matrices, arXiv:1406.7788 [math.CO], 2014.
• Index entries for linear recurrences with constant coefficients, signature (1,1,3).

Crossrefs

Cf. A077947, A081578.

Programs

Mathematica

LinearRecurrence[{1, 1, 3}, {0, 0, 1}, 50]  (* Vladimir Joseph Stephan Orlovsky, May 25 2011 *)

Formula

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

Extensions

Name clarified by Michel Marcus, Aug 07 2022