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

0,9

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).

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

Example

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

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 *)

Prog

(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
(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

Crossrefs

Cf. A245332, A245487.

Sequence in context: A332342 A173539 A292250 * A298203 A298209 A211871

Adjacent sequences: A245489 A245490 A245491 * A245493 A245494 A245495

Keyword

nonn,easy

Author

David Neil McGrath, Jul 24 2014

Extensions

More terms from Colin Barker, Jul 24 2014

Status

approved