A075111 a(n) = Sum_{i=0..floor(n/2)} (-1)^(i+floor(n/2))*T(2i+e), where T(n) are tribonacci numbers (A000073) and e = (1/2)(1-(-1)^n).

0, 1, 1, 1, 3, 6, 10, 18, 34, 63, 115, 211, 389, 716, 1316, 2420, 4452, 8189, 15061, 27701, 50951, 93714, 172366, 317030, 583110, 1072507, 1972647, 3628263, 6673417, 12274328, 22576008, 41523752, 76374088, 140473849, 258371689

Offset: 0

Author

Mario Catalani (mario.catalani(AT)unito.it), Sep 01 2002

Keywords

• easy
• nonn

Comments

a(n) is the convolution of T(n) with the sequence (1,0,-1,0,1,0,-1,0,....) A056594.

The number of ways to place non-overlapping Young diagrams of shape (3,1) on an 3 by n rectangle. - Per Alexandersson, Jul 01 2025

Links

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

Crossrefs

Cf. A000073, A056594, A074662, A074677, A074678.

Programs

Mathematica

CoefficientList[Series[x/(1 - x - 2*x^3 - x^4 - x^5), {x, 0, 40}], x]

Formula

a(n) = a(n-1)+2a(n-3)+a(n-4)+a(n-5), a(0)=0, a(1)=1, a(2)=1, a(3)=1, a(4)=3.

G.f.: x/(1 - x - 2*x^3 - x^4 - x^5).