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A062202 Number of compositions of n such that two adjacent parts are not equal modulo 4. 1
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 (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^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: A214286 A108700 A325851 * A049859 A124636 A231337

Adjacent sequences:  A062199 A062200 A062201 * A062203 A062204 A062205

KEYWORD

nonn

AUTHOR

Vladeta Jovovic, Jun 13 2001

STATUS

approved

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Last modified January 21 04:53 EST 2020. Contains 331104 sequences. (Running on oeis4.)