A210342 Row sums of triangle A210341.

1, 2, 4, 9, 24, 78, 317, 1636, 10752, 89871, 955536, 12930172, 222618065, 4874855542, 135781292308, 4811103270053, 216847500834512, 12432143862756778, 906625645142897789, 84102571511631809864, 9923979699312024569440, 1489546408205976627946331

Offset: 0

Author

Emanuele Munarini, Mar 20 2012

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..100

Crossrefs

Cf. A210341.

Programs

Magma

[&+[Fibonacci(n-k+2)^k: k in [0..n]]: n in [0..21]]; // Bruno Berselli, Mar 28 2012

Mathematica

Table[Sum[Fibonacci[n - k + 2]^k, {k, 0, n}], {n, 0, 100}]

Maxima

makelist(sum(fib(n-k+2)^k,k,0,n),n,0,12);

Formula

G.f.: Sum_{k>=0} x^k/(1-Fibonacci(k+2)*x).

a(n) = [x^n] Sum_{k=0..n} x^k/(1-Fibonacci(k+2)*x).

a(n) = A135961(n+2)-1. - Vaclav Kotesovec, Jan 05 2013