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A245492 Number of compositions of n into parts 3 and 5 with at least one 3 and one 5. 4
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 (list; graph; refs; listen; history; text; internal format)
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: A086834 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

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Last modified November 13 12:45 EST 2019. Contains 329094 sequences. (Running on oeis4.)