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A062203 Number of compositions of n such that two adjacent parts are not equal modulo 5. 3
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 (list; graph; refs; listen; history; text; internal format)
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 * A095063 A003242 A073728

Adjacent sequences:  A062200 A062201 A062202 * A062204 A062205 A062206

KEYWORD

nonn

AUTHOR

Vladeta Jovovic, Jun 13 2001

STATUS

approved

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Last modified January 22 12:13 EST 2019. Contains 319363 sequences. (Running on oeis4.)