OFFSET
0,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..5000
FORMULA
G.f.: Sum_{i>=2} Fibonacci(i)*x^Fibonacci(i)/(1 - x^Fibonacci(i)) / Product_{j>=1} (1 - x^j). - Ilya Gutkovskiy, Feb 01 2017
EXAMPLE
For n = 6 we have:
--------------------------------------
. Sum of
Partitions Fibonacci parts
--------------------------------------
6 .......................... 0
3 + 3 ...................... 6
4 + 2 ...................... 2
2 + 2 + 2 .................. 6
5 + 1 ...................... 6
3 + 2 + 1 .................. 6
4 + 1 + 1 .................. 2
2 + 2 + 1 + 1 .............. 6
3 + 1 + 1 + 1 .............. 6
2 + 1 + 1 + 1 + 1 .......... 6
1 + 1 + 1 + 1 + 1 + 1 ...... 6
------------------------------------
Total ..................... 52
So a(6) = 52.
MAPLE
b:= proc(n, i) option remember; `if`(n=0, [1, 0], `if`(i<1, 0,
`if`(i>n, 0, ((p, m)-> p +`if`(issqr(m+4) or issqr(m-4),
[0, p[1]*i], 0))(b(n-i, i), 5*i^2)) +b(n, i-1)))
end:
a:= n-> b(n$2)[2]:
seq(a(n), n=0..50); # Alois P. Heinz, Feb 01 2017
MATHEMATICA
max = 42; F = Fibonacci; gf = Sum[F[i]*x^F[i]/(1-x^F[i]), {i, 2, max}] / Product[1-x^j, {j, 1, max}] + O[x]^max; CoefficientList[gf, x] (* Jean-François Alcover, Feb 21 2017, after Ilya Gutkovskiy *)
b[n_, i_] := b[n, i] = If[n==0, {1, 0}, If[i<1, 0, If[i>n, 0, Function[{p, m}, p+If[IntegerQ @ Sqrt[m+4] || IntegerQ @ Sqrt[m-4], {0, p[[1]]*i}, 0] ][b[n-i, i], 5*i^2]]+b[n, i-1]]]; a[n_] := b[n, n][[2]]; Table[a[n], {n, 0, 50}] (* Jean-François Alcover, Feb 21 2017, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Omar E. Pol, Nov 21 2011
EXTENSIONS
More terms from Alois P. Heinz, Nov 21 2011
STATUS
approved