A062202 - OEIS

A062202

Number of compositions of n such that two adjacent parts are not equal modulo 4.

1, 1, 1, 3, 4, 7, 12, 22, 33, 57, 103, 169, 277, 479, 824, 1368, 2306, 3941, 6657, 11206, 18998, 32194, 54325, 91880, 155633, 263120, 444674, 752545, 1273278, 2152704, 3640801, 6159723, 10418147, 17618849, 29802480, 50410743, 85259765

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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^4-x-1)*(x^4-x^2-1)*(x^4-x^3-1)/(x^16-x^15-x^14-3*x^12+3*x^11+x^10+2*x^9+6*x^8-x^7-3*x^6-2*x^5-5*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-A062203.

Sequence in context: A340359 A108700 A325851 * A049859 A124636 A231337

Adjacent sequences: A062199 A062200 A062201 * A062203 A062204 A062205

KEYWORD

nonn

AUTHOR

Vladeta Jovovic, Jun 13 2001

STATUS

approved