A245367 Compositions of n into parts 3, 5 and 7.

1, 0, 0, 1, 0, 1, 1, 1, 2, 1, 3, 3, 3, 6, 5, 8, 10, 11, 17, 18, 25, 32, 37, 52, 61, 79, 102, 123, 163, 200, 254, 326, 402, 519, 649, 819, 1045, 1305, 1664, 2096, 2643, 3358, 4220, 5352, 6759, 8527, 10806, 13622, 17237, 21785, 27501, 34802, 43934, 55544, 70209, 88672, 112131, 141644, 179018, 226274, 285860, 361358

Offset

0,9

Links

Table of n, a(n) for n=0..61.

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

Formula

G.f: 1/(1-x^3-x^5-x^7).

a(n) = a(n-3) + a(n-5) + a(n-7).

Example

a(16) = 10: the compositions are the permutations of [5533] (there are 4!/2!2!=6 of them) and the permutations of [7333] (there are 4!/3!=4).

Mathematica

LinearRecurrence[{0, 0, 1, 0, 1, 0, 1}, {1, 0, 0, 1, 0, 1, 1}, 70] (* Harvey P. Dale, Jan 27 2017 *)

Prog

(PARI)  Vec(1/(1-x^3-x^5-x^7) +O(x^66)) \\ Joerg Arndt, Aug 20 2014

Crossrefs

Cf. A000073, A013979, A017818, A060945, A079956, A079957, A079971, A079973, A120400, A121833.

Sequence in context: A341147 A325335 A262952 * A304740 A326619 A326567

Adjacent sequences: A245364 A245365 A245366 * A245368 A245369 A245370

Keyword

nonn,easy

Author

David Neil McGrath, Aug 20 2014

Status

approved