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
Keywords
Examples
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.
Links
- Alois P. Heinz, Table of n, a(n) for n = 0..27
Programs
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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 *)
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
Comments