A062203 Number of compositions of n such that two adjacent parts are not equal modulo 5.

1, 1, 1, 3, 4, 7, 14, 21, 38, 65, 110, 195, 329, 564, 975, 1675, 2885, 4950, 8503, 14627, 25158, 43255, 74325, 127775, 219662, 377662, 649313, 1116085, 1918690, 3298498, 5670521, 9748641, 16758575, 28809772, 49527786, 85143986, 146373609

Offset: 0

Author

Vladeta Jovovic, Jun 13 2001

Keywords

• nonn

References

• I. P. Goulden and D. M. Jackson, Combinatorial Enumeration, Wiley, N.Y., 1983, (Problem 2.4.13).

Crossrefs

Cf. A003242, A062200-A062202.

Formula

G.f.: -(x^5-x-1)*(x^5-x^2-1)*(x^5-x^3-1)*(x^5-x^4-1) / (x^25 -x^24-x^23 -3*x^20+3*x^19 +3*x^18+x^17 +x^16+9*x^15 -5*x^14-5*x^13 -5*x^12-5*x^11 -9*x^10+2*x^9 +2*x^8+4*x^7 +4*x^6+7*x^5 +x^4+x^3-1). Generally, g.f. for the number of compositions of n such that two adjacent parts are not equal modulo p is 1/(1-Sum_{i=1..p} x^i/(1+x^i-x^p)).