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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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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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: A149359 A167402 A060897 this_sequence A149360 A149361 A149362
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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N. J. A. Sloane (njas(AT)research.att.com).
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