A098641 Number of partitions of the n-th Fibonacci number into Fibonacci numbers.

1, 1, 1, 2, 3, 6, 14, 41, 157, 803, 5564, 53384, 718844, 13783708, 380676448, 15298907733, 902438020514, 78720750045598, 10220860796171917, 1986422867300209784, 580763241873718042562, 256553744608217295298827, 171912553856721407543178940, 175350753369071026461010505478

Offset

0,4

Comments

a(n) = A003107(A000045(n)).

Links

Alois P. Heinz, Table of n, a(n) for n = 0..27

Formula

a(n) = A098642(n) + A098643(n) + A098644(n).

Example

n=6: A000045(6)=8, a(6) = #{8, 5+3, 5+2+1, 5+1+1+1, 3+3+2, 3+3+1+1, 3+2+2+1, 3+2+1+1+1, 3+1+1+1+1+1, 2+2+2+2, 2+2+2+1+1, 2+2+1+1+1+1, 2+1+1+1+1+1+1, 1+1+1+1+1+1+1+1} = 14; the other partitions of 8 into parts with at least one non-Fibonacci number: 7+1, 6+2, 6+1+1, 4+4, 4+3+1, 4+2+2, 4+2+1+1 and 4+1+1+1+1.

Mathematica

cl = CoefficientList[ Series[1/Product[(1 - x^Fibonacci[i]), {i, 2, 21}], {x, 0, 10950}], x]; cl[[ Table[ Fibonacci[i] + 1, {i, 21}] ]] (* Robert G. Wilson v, Apr 25 2005 *)

Crossrefs

Cf. A000041, A000045, A065033, A072214, A098642, A098643, A098644, A319503.

Sequence in context: A081293 A193215 A007611 * A188775 A015892 A056569

Adjacent sequences: A098638 A098639 A098640 * A098642 A098643 A098644

Keyword

nonn

Author

Marcel Dubois de Cadouin (dubois.ml(AT)club-internet.fr), Oct 27 2004

Extensions

Corrected and extended by Reinhard Zumkeller, Apr 24 2005

a(15)-a(21) from Robert G. Wilson v, Apr 25 2005

Entry revised by N. J. A. Sloane, Mar 29 2006

a(0), a(22)-a(23) from Alois P. Heinz, Sep 20 2018

Status

approved