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A245367
Compositions of n into parts 3, 5 and 7.
2
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
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
KEYWORD
nonn,easy
AUTHOR
David Neil McGrath, Aug 20 2014
STATUS
approved