A245492 Number of compositions of n into parts 3 and 5 with at least one 3 and one 5.

0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 3, 0, 3, 4, 0, 6, 5, 4, 10, 6, 10, 15, 12, 20, 21, 23, 35, 34, 44, 56, 57, 80, 91, 101, 137, 148, 181, 230, 249, 318, 379, 430, 549, 629, 748, 928, 1060, 1298, 1557, 1809, 2226, 2617, 3109, 3783, 4426, 5336, 6400, 7536, 9120

Offset: 0

Author

David Neil McGrath, Jul 24 2014

Keywords

• nonn
• easy

Examples

			a(20)=6, the tuples being: (533333),(353333),(335333),(333533),(333353),(333335).
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (-1, -1, 1, 1, 3, 2, 2, -1, -1, -2, -1, -1).

Crossrefs

Cf. A245332, A245487.

Programs

Haskell

a245492 n = a245492_list !! (n-1)
a245492_list = [0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 3, 0] ++
               zipWith3 (((+) .) . (+))
               (drop 8 a245492_list) (drop 10 a245492_list)
               (cycle [1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 2, 0, 0, 1, 0])
-- Reinhard Zumkeller, Jul 28 2014

Mathematica

CoefficientList[Series[x^8*(x^4 + x^3 + 2*x^2 + 2*x + 2)/((x - 1)*(x^2 + x + 1)*(x^4 + x^3 + x^2 + x + 1)*(x^5 + x^3 - 1)), {x, 0, 60}], x] (* Wesley Ivan Hurt, Jul 24 2014 *)

PARI

a=[0,0,0,0,0,0,0,2,0,0,3,0]; b=[1,1,0,0,1,1,0,1,0,0,2,0,0,1,0]; k=1; for(n=13, 100, a=concat(a, a[n-3]+a[n-5]+b[k]); if(k==#b, k=1, k++)); a \\ Colin Barker, Jul 24 2014

Formula

a(n) = a(n-3)+a(n-5)+b(n) where b(n) is the 15-cycle: (1,1,0,0,1,1,0,1,0,0,2,0,0,1,0) with b(n)=b(n-15) starting at b(13)=1. e.g. b(28)=b(13). The initial values for a(n) are: a(8)=2, a(9)=0, a(10)=0, a(11)=3, a(12)=0.

G.f.: x^8*(x^4+x^3+2*x^2+2*x+2) / ((x-1)*(x^2+x+1)*(x^4+x^3+x^2+x+1)*(x^5+x^3-1)). - Colin Barker, Jul 24 2014

Extensions

More terms from Colin Barker, Jul 24 2014