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

0,4

References

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

Links

Table of n, a(n) for n=0..36.

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)).

Crossrefs

Cf. A003242, A062200-A062202.

Sequence in context: A121174 A050071 A041002 * A319548 A095063 A003242

Adjacent sequences: A062200 A062201 A062202 * A062204 A062205 A062206

Keyword

nonn

Author

Vladeta Jovovic, Jun 13 2001

Status

approved