A245527 Number of compositions of n into parts 4 and 5 with at least one 4 and one 5.

0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 3, 3, 0, 0, 4, 6, 4, 0, 5, 10, 10, 5, 6, 15, 20, 15, 13, 21, 35, 35, 29, 35, 56, 70, 65, 64, 92, 126, 136, 129, 156, 219, 263, 265, 285, 375, 484, 528, 550, 660, 860, 1013, 1078, 1210, 1521, 1873, 2092, 2288, 2732, 3394

Offset

0,10

Links

Table of n, a(n) for n=0..62.

Index entries for linear recurrences with constant coefficients, signature (-1, -1, -1, 1, 3, 3, 3, 2, -1, -2, -2, -2, -1).

Formula

a(n) = a(n-4)+a(n-5)+b(n) where b(n) is the 20-cycle (1,0,0,1,0,1,0,1,0,0,1,1,0,0,0,2,0,0,0,1) and b(n)=b(n-20). Initial values are b(14)=1, a(9)=2, a(10)=0, a(11)=0, a(12)=0, a(13)=3.

G.f.: 1+1/(1-x^5-x^4)-1/(1-x^5)-1/(1-x^4) (see comment A245332). - courtesy of Joerg Arndt

Example

a(22)=10 The tuples are (55444)(54544)(54454)... where a(22)=5!/3!2!=10.

Mathematica

CoefficientList[Series[1 + 1/(1 - x^5 - x^4) - 1/(1 - x^5) - 1/(1 - x^4), {x, 0, 60}], x] (* Wesley Ivan Hurt, Jul 26 2014 *)

Crossrefs

Cf. A245332, A245492, A245487.

Sequence in context: A280683 A171871 A076260 * A287871 A336644 A135416

Adjacent sequences: A245524 A245525 A245526 * A245528 A245529 A245530

Keyword

nonn,easy

Author

David Neil McGrath, Jul 25 2014

Status

approved