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Search: id:A062200
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| A062200 |
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Number of compositions of n such that two adjacent parts are not equal modulo 2. |
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+0
6
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| 1, 1, 1, 3, 2, 6, 6, 11, 16, 22, 37, 49, 80, 113, 172, 257, 377, 573, 839, 1266, 1874, 2798, 4175, 6204, 9274, 13785, 20577, 30640, 45665, 68072, 101393, 151169, 225193, 335659, 500162, 745342, 1110790, 1655187, 2466760, 3675822
(list; graph; listen)
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OFFSET
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0,4
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COMMENT
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Also (0,1)-strings such that all maximal blocks of 1's have even length and all maximal blocks of 0's have odd length.
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REFERENCES
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I. P. Goulden and D. M. Jackson, Combinatorial Enumeration, Wiley, N.Y., 1983,(Problems 2.4.3, 2.4.13).
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FORMULA
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a(n)= Sum_{j=0..n+1} binomial(n-j+1, 3*j-n+1). a(n) = 2*a(n-2)+a(n-3)-a(n-4).
G.f.: -(x^2-x-1)/(x^4-x^3-2*x^2+1). More 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)).
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CROSSREFS
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Cf. A003242, A062201-A062203.
Sequence in context: A154028 A157793 A096375 this_sequence A114208 A014686 A053090
Adjacent sequences: A062197 A062198 A062199 this_sequence A062201 A062202 A062203
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KEYWORD
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nonn
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AUTHOR
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Vladeta Jovovic (vladeta(AT)eunet.rs), Jun 13 2001
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