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A319395 Number of partitions of n into exactly two positive Fibonacci numbers. 3
0, 0, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 0, 1, 1, 1, 2, 0, 1, 0, 0, 1, 1, 1, 1, 0, 2, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..17711

FORMULA

a(n) = [x^n y^2] 1/Product_{j>=2} (1-y*x^A000045(j)).

MAPLE

h:= proc(n) option remember; `if`(n<1, 0, `if`((t->

      issqr(t+4) or issqr(t-4))(5*n^2), n, h(n-1)))

    end:

b:= proc(n, i, t) option remember; `if`(n=0, 1, `if`(i<1 or

      t<1, 0, b(n, h(i-1), t)+b(n-i, h(min(n-i, i)), t-1)))

    end:

a:= n-> (k-> b(n, h(n), k)-b(n, h(n), k-1))(2):

seq(a(n), n=0..120);

MATHEMATICA

h[n_] := h[n] = If[n < 1, 0, If[Function[t, IntegerQ@Sqrt[t + 4] || IntegerQ@Sqrt[t - 4]][5 n^2], n, h[n - 1]]];

b[n_, i_, t_] := b[n, i, t] = If[n == 0, 1, If[i < 1 || t < 1, 0, b[n, h[i - 1], t] + b[n - i, h[Min[n - i, i]], t - 1]]];

a[n_] := With[{k = 2}, b[n, h[n], k] - b[n, h[n], k - 1]];

a /@ Range[0, 120] (* Jean-Fran├žois Alcover, Dec 07 2020, after Alois P. Heinz *)

CROSSREFS

Column k=2 of A319394.

Cf. A000045.

Sequence in context: A257886 A144477 A106345 * A194636 A286299 A081729

Adjacent sequences:  A319392 A319393 A319394 * A319396 A319397 A319398

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Sep 18 2018

STATUS

approved

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Last modified September 19 16:34 EDT 2021. Contains 347564 sequences. (Running on oeis4.)