|
Search: id:A007000
|
|
|
| A007000 |
|
Number of partitions of n into Fibonacci parts (with 2 types of 1).
(Formerly M1045)
|
|
+0
3
|
|
| 1, 2, 4, 7, 11, 17, 25, 35, 49, 66, 88, 115, 148, 189, 238, 297, 368, 451, 550, 665, 799, 956, 1136, 1344, 1583, 1855, 2167, 2520, 2920, 3373, 3882, 4455, 5097, 5814, 6617, 7509, 8502, 9604, 10823, 12173, 13662, 15302, 17110, 19093, 21271, 23657, 26266
(list; graph; listen)
|
|
|
OFFSET
|
0,2
|
|
|
REFERENCES
|
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
|
|
LINKS
|
T. D. Noe, Table of n, a(n) for n=0..1000
|
|
FORMULA
|
a(n)=1/n*Sum_{k=1..n} (A005092(k)+1)*a(n-k), n > 1, a(0)=1. - Vladeta Jovovic (vladeta(AT)eunet.rs), Aug 22 2002
G.f.=1/product(1-x^fibonacci(j), j=1..infinity). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 05 2006
|
|
EXAMPLE
|
a(2)=4 because we have [2],[1',1'],[1',1],[1,1] (the two types of 1 are denoted 1 and 1').
|
|
MAPLE
|
with(combinat): gf := 1/product((1-q^fibonacci(k)), k=1..20): s := series(gf, q, 200): for i from 0 to 199 do printf(`%d, `, coeff(s, q, i)) od:
|
|
MATHEMATICA
|
CoefficientList[ Series[ 1/Product[1 - x^Fibonacci[i], {i, 1, 15}], {x, 0, 50}], x]
|
|
CROSSREFS
|
Cf. A003107.
Sequence in context: A028291 A067997 A034379 this_sequence A073472 A096914 A004250
Adjacent sequences: A006997 A006998 A006999 this_sequence A007001 A007002 A007003
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
N. J. A. Sloane (njas(AT)research.att.com), Mira Bernstein
|
|
EXTENSIONS
|
More terms and Maple code from James A. Sellers (sellersj(AT)math.psu.edu), Feb 08, 2002
|
|
|
Search completed in 0.002 seconds
|
