A245368 Compositions of n into parts 3, 4 and 7.

1, 0, 0, 1, 1, 0, 1, 3, 1, 1, 5, 5, 2, 7, 13, 8, 10, 25, 26, 20, 42, 64, 54, 72, 131, 144, 146, 245, 339, 344, 463, 715, 827, 953, 1423, 1881, 2124, 2839, 4019, 4832, 5916, 8281, 10732, 12872, 17036, 23032, 28436, 35824, 48349, 62200, 77132, 101209, 133581

Offset: 0

Author

David Neil McGrath, Aug 20 2014

Keywords

• nonn
• easy

Examples

			a(14) = 13. The compositions (ordered partitions) of 14 into parts 3, 4 and 7 are the permutations of (7,7) (there is only one), the permutations of (7,4,3) (there are 3!=6 of these) and the permutations of (4,4,3,3) (there are 4!/2!2!=6 of these).
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (0,0,1,1,0,0,1).

Crossrefs

Cf. A017818, A079956.

Programs

Magma

I:=[1,0,0,1,1,0,1]; [n le 7 select I[n] else Self(n-3)+Self(n-4)+Self(n-7): n in [1..60]]; // Vincenzo Librandi, Jan 08 2016

Maple

a:= proc(n) option remember; `if`(n=0, 1,
      `if`(n<0, 0, add(a(n-j), j=[3, 4, 7])))
    end:
seq(a(n), n=0..80);  # Alois P. Heinz, Aug 21 2014

Mathematica

LinearRecurrence[{0, 0, 1, 1, 0, 0, 1}, {1, 0, 0, 1, 1, 0, 1}, 60] (* Jean-François Alcover, Jan 08 2016 *)

Formula

G.f: 1/(1-x^3-x^4-x^7).

a(n) = a(n-3) + a(n-4) + a(n-7).