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A208481
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Diagonal sums of triangle A185384.
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2
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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
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0,2
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LINKS
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FORMULA
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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).
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MATHEMATICA
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Table[Sum[Binomial[n-k, k]Fibonacci[2n-3k+1], {k, 0, Floor[n/2]}], {n, 0, 100}]
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PROG
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(Maxima) makelist(sum(binomial(n-k, k)*fib(2*n-3*k+1), k, 0, floor(n/2)), n, 0, 27);
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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