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

0,9

Links

Table of n, a(n) for n=0..64.

Index entries for linear recurrences with constant coefficients, signature (0,0,1,0,1,0,0,0,1).

Formula

G.f.: 1/(1-x^3-x^5-x^9).

a(n) = a(n-3) + a(n-5) + a(n-9).

Example

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).

Prog

(PARI) Vec( 1/(1-x^3-x^5-x^9) +O(x^66) ) \\ Joerg Arndt, Aug 24 2014

Crossrefs

Cf. A079957, A245367, A245369.

Sequence in context: A240127 A109524 A191521 * A321341 A377305 A284549

Adjacent sequences: A245367 A245368 A245369 * A245371 A245372 A245373

Keyword

nonn,easy

Author

David Neil McGrath, Aug 24 2014

Status

approved