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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

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OFFSET

0,2

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).

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).

MATHEMATICA

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