A208481 Diagonal sums of triangle A185384.

1, 2, 6, 19, 60, 188, 589, 1846, 5786, 18135, 56840, 178152, 558377, 1750106, 5485310, 17192459, 53885860, 168892996, 529356757, 1659148590, 5200224626, 16298923631, 51085276240, 160115201936, 501844754065, 1572918462066, 4929955864374, 15451827549123

Offset: 0

Author

Emanuele Munarini, Feb 29 2012

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (3,0,1,1).

Crossrefs

Cf. A185384.

Programs

Mathematica

Table[Sum[Binomial[n-k,k]Fibonacci[2n-3k+1],{k,0,Floor[n/2]}],{n,0,100}]

Maxima

makelist(sum(binomial(n-k,k)*fib(2*n-3*k+1),k,0,floor(n/2)),n,0,27);

Formula

a(n) = Sum_{k=0..floor(n/2)} binomial(n-k,k)*F(2*n-3*k+1), where F(n) are the Fibonacci numbers (A000045).

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

a(n) = 3*a(n-1) + a(n-3) + a(n-4).