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Search: id:A005190
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| A005190 |
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Central quadrinomial coefficients: largest coefficient of (1+x+x^2+x^3)^n.
(Formerly M3456)
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+0
11
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| 1, 1, 4, 12, 44, 155, 580, 2128, 8092, 30276, 116304, 440484, 1703636, 6506786, 25288120, 97181760, 379061020, 1463609356, 5724954544, 22187304112, 86981744944, 338118529539, 1327977811076, 5175023913008, 20356299454276
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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The maximal coefficient is that of x^[3n/2]. - M. F. Hasler (Maximilian.Hasler(AT)gmail.com), Jul 23 2007
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REFERENCES
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L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 78.
V. E. Hoggatt, Jr., and M. Bicknell, Diagonal sums of generalized Pascal triangles, Fib. Quart., 7 (1969), 341-358, 393.
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..200
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FORMULA
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lim n -> infinity a(n+1)/a(n) = 4; for n>2 a(n+1) < 4*a(n) - Benoit Cloitre (benoit7848c(AT)orange.fr), Sep 28 2002
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PROGRAM
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(PARI) a(n)=vecmax(vector(3*n, i, polcoeff((1+x+x^2+x^3)^n, i, x)))
(PARI) A005190(n)=polcoeff((1+x+x^2+x^3)^n, (3*n)>>1) \\ M. F. Hasler
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CROSSREFS
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Cf. A001405, A002426, A005191, A018901, A025012, A025013, A025014
Sequence in context: A100217 A003444 A060897 this_sequence A055542 A000759 A076793
Adjacent sequences: A005187 A005188 A005189 this_sequence A005191 A005192 A005193
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KEYWORD
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nonn,easy
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AUTHOR
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njas
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