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Search: id:A035343
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| A035343 |
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Triangle of coefficients in expansion of (1+x+x^2+x^3+x^4)^n. |
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+0
10
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| 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 4, 3, 2, 1, 1, 3, 6, 10, 15, 18, 19, 18, 15, 10, 6, 3, 1, 1, 4, 10, 20, 35, 52, 68, 80, 85, 80, 68, 52, 35, 20, 10, 4, 1, 1, 5, 15, 35, 70, 121, 185, 255, 320, 365, 381, 365, 320, 255, 185, 121, 70, 35, 15, 5, 1, 1, 6, 21, 56, 126, 246, 426, 666
(list; graph; listen)
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OFFSET
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0,8
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COMMENT
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Coefficient of x^k in (1+x+x^2+x^3+x^4)^n is the number of distinct ways in which k unlabeled objects can be distributed in n labeled urns allowing at most 4 objects to fall in each urn. - Nour-Eddine Fahssi (fahssin(AT)yahoo.fr), Mar 16 2008
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REFERENCES
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L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 78.
D. C. Fielder and C. O. Alford, Pascal's triangle: top gun or just one of the gang?, in G E Bergum et al., eds., Applications of Fibonacci Numbers Vol. 4 1991 pp. 77-90 (Kluwer).
Freund, J. E., Restricted Occupancy Theory - A Generalization of Pascal's Triangle, American Mathematical Monthly, Vol. 63, No. 1 (1956), pp. 20-27.
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LINKS
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S. Finch, P. Sebah and Z.-Q. Bai, Odd Entries in Pascal's Trinomial Triangle (arXiv:0802.2654)
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EXAMPLE
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1; 1,1,1,1,1; 1,2,3,4,5,4,3,2,1; ...
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CROSSREFS
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Cf. A007318, A027907, A008287.
Sequence in context: A125746 A017890 A134011 this_sequence A017880 A086144 A131974
Adjacent sequences: A035340 A035341 A035342 this_sequence A035344 A035345 A035346
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KEYWORD
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nonn,tabf,easy
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AUTHOR
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njas
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EXTENSIONS
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More terms from James A. Sellers (sellersj(AT)math.psu.edu)
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