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Search: id:A000102
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| A000102 |
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a(n) = number of compositions of n in which the maximum part size is 4.
(Formerly M1409 N0551)
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+0
3
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| 0, 0, 0, 0, 1, 2, 5, 12, 27, 59, 127, 269, 563, 1167, 2400, 4903, 9960, 20135, 40534, 81300, 162538, 324020, 644282, 1278152, 2530407, 5000178, 9863763, 19427976, 38211861, 75059535, 147263905, 288609341, 565047233, 1105229439, 2159947998
(list; graph; listen)
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OFFSET
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0,6
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REFERENCES
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J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 155.
J. L. Yucas, Counting special sets of binary Lyndon words, Ars Combin., 31 (1991), 21-29.
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..200
Nick Hobson, Python program for this sequence
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FORMULA
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G.f.: x^4/(1-x-x^2-x^3)/(1-x-x^2-x^3-x^4).
a(n)=2*a(n-1)+a(n-2)-2*a(n-4)-3*a(n-5)-2*a(n-6)-a(n-7). Convolution of Tribonacci and Tetranacci numbers (A000073 and A000078). - Frank Adams-Watters (FrankTAW(AT)Netscape.net), Jan 13 2006
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EXAMPLE
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For example, a(6)=5 counts 1+1+4, 2+4, 4+2, 4+1+1, 1+4+1. - David Callan (callan(AT)stat.wisc.edu), Dec 09 2004
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CROSSREFS
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Sequence in context: A129983 A083378 A116712 this_sequence A086589 A091596 A077863
Adjacent sequences: A000099 A000100 A000101 this_sequence A000103 A000104 A000105
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KEYWORD
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nonn,nice,easy
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AUTHOR
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njas
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EXTENSIONS
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More terms from Sascha Kurz (sascha.kurz(AT)uni-bayreuth.de), Aug 15 2002
Definition improved by David Callan and Frank Adams-Watters.
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