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A343537 Number of partitions of the n-th Fibonacci number into a Fibonacci number of Fibonacci parts. 1
1, 1, 1, 2, 3, 5, 7, 16, 41, 135, 632, 4091, 37020, 478852, 8897512, 240133480, 9489055662, 552854898873, 47794151866058, 6165361571608551, 1192709563056788508, 347571453153709529743, 153189847887607116894958 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Table of n, a(n) for n=0..22.

FORMULA

a(n) = Sum_{k in {A000045}} A319394(A000045(n),k).

EXAMPLE

a(5) = 5: [5], [3,2], [3,1,1], [2,2,1], [1,1,1,1,1].  Partition [2,1,1,1] is not counted because 4 (the number of parts) is not a Fibonacci number.

a(6) = 7: [8], [5,3], [5,2,1], [3,3,2], [3,2,1,1,1], [2,2,2,1,1], [1,1,1,1,1,1,1,1].

a(7) = 16: [13], [8,5], [8,3,2], [8,2,1,1,1], [5,5,3], [5,5,1,1,1], [5,3,3,1,1], [5,3,2,2,1], [5,2,2,2,2], [5,2,1,1,1,1,1,1], [3,3,3,3,1], [3,3,3,2,2], [3,3,2,1,1,1,1,1], [3,2,2,2,1,1,1,1], [2,2,2,2,2,1,1,1], [1,1,1,1,1,1,1,1,1,1,1,1,1].

MAPLE

f:= n-> (t-> issqr(t+4) or issqr(t-4))(5*n^2):

h:= proc(n) option remember; `if`(f(n), n, h(n-1)) end:

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

      f(c+n), 1, 0), b(n-i, h(min(n-i, i)), c+1)+b(n, h(i-1), c))

    end:

a:= n-> b((<<0|1>, <1|1>>^n)[1, 2]$2, 0):

seq(a(n), n=0..17);

CROSSREFS

Cf. A000045, A098641, A316154, A319394, A344790.

Sequence in context: A319913 A094575 A145968 * A192579 A215658 A295266

Adjacent sequences:  A343534 A343535 A343536 * A343538 A343539 A343540

KEYWORD

nonn

AUTHOR

Alois P. Heinz, May 26 2021

STATUS

approved

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Last modified September 24 21:05 EDT 2021. Contains 347651 sequences. (Running on oeis4.)