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Search: id:A005725
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| A005725 |
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Quadrinomial coefficients.
(Formerly M2843)
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+0
3
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| 1, 1, 3, 10, 31, 101, 336, 1128, 3823, 13051, 44803, 154518, 534964, 1858156, 6472168, 22597760, 79067375, 277164295, 973184313, 3422117190, 12049586631, 42478745781, 149915252028, 529606271560, 1872653175556, 6627147599476
(list; graph; listen)
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OFFSET
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0,3
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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.
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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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Coefficient of x^n in (1+x+x^2+x^3)^n.
a(n)=sum(i+j+k=n, 0<=k<=j<=i<=n, binomial(n, i)*binomial(i, j)*binomial(j, k)) - Benoit Cloitre (benoit7848c(AT)orange.fr), Jun 06 2004
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MAPLE
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seq( sum('binomial(n, 2*k)*binomial(n, k)', 'k'=0..floor(n/2)), n=0..30 ); # Detlef Pauly (dettodet(AT)yahoo.de), Nov 09 2001
a:=n->sum(binomial(n, 1*j)*binomial(n, 2*j), j=0..n): seq(a(n), n=1..25); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Feb 12 2007
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CROSSREFS
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Sequence in context: A114487 A017934 A005510 this_sequence A079522 A024426 A034016
Adjacent sequences: A005722 A005723 A005724 this_sequence A005726 A005727 A005728
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KEYWORD
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nonn,easy,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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More terms from James A. Sellers (sellersj(AT)math.psu.edu), Jul 12 2000
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