A245370 Number of compositions of n into parts 3, 5 and 9.
1, 0, 0, 1, 0, 1, 1, 0, 2, 2, 1, 3, 3, 3, 6, 5, 6, 11, 10, 13, 19, 19, 27, 35, 37, 52, 65, 74, 100, 121, 145, 192, 230, 282, 365, 440, 548, 695, 843, 1058, 1327, 1621, 2035, 2535, 3119, 3910, 4851, 5997, 7503, 9297, 11528, 14389, 17829, 22150, 27596, 34208, 42536, 52928, 65655, 81660, 101525, 126020, 156738, 194776, 241888
Offset: 0
Examples
a(28)=100 The compositions of n into parts 3,5 and 9 are the permutations of (9955)(these are 4!/2!2!=6), (555553) (these are 6!/5!=6), (955333) (these are 6!/3!2!=60), (55333333) (these are 8!/6!2!=28).
Links
- Index entries for linear recurrences with constant coefficients, signature (0,0,1,0,1,0,0,0,1).
Programs
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PARI
Vec( 1/(1-x^3-x^5-x^9) +O(x^66) ) \\ Joerg Arndt, Aug 24 2014
Formula
G.f.: 1/(1-x^3-x^5-x^9).
a(n) = a(n-3) + a(n-5) + a(n-9).