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

0,2

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}]

Prog

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

Crossrefs

Cf. A185384.

Sequence in context: A183188 A118364 A294500 * A052544 A204200 A371708

Adjacent sequences: A208478 A208479 A208480 * A208482 A208483 A208484

Keyword

nonn,easy

Author

Emanuele Munarini, Feb 29 2012

Status

approved