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Compositions of n into parts 3, 5 and 7.
2

%I #21 Jan 27 2017 14:47:42

%S 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,

%T 123,163,200,254,326,402,519,649,819,1045,1305,1664,2096,2643,3358,

%U 4220,5352,6759,8527,10806,13622,17237,21785,27501,34802,43934,55544,70209,88672,112131,141644,179018,226274,285860,361358

%N Compositions of n into parts 3, 5 and 7.

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,1,0,1,0,1).

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

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

%e 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).

%t LinearRecurrence[{0,0,1,0,1,0,1},{1,0,0,1,0,1,1},70] (* _Harvey P. Dale_, Jan 27 2017 *)

%o (PARI) Vec(1/(1-x^3-x^5-x^7) +O(x^66)) \\ _Joerg Arndt_, Aug 20 2014

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

%K nonn,easy

%O 0,9

%A _David Neil McGrath_, Aug 20 2014