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Search: id:A008287
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| A008287 |
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Triangle of quadrinomial coefficients. |
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14
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| 1, 1, 1, 1, 1, 1, 2, 3, 4, 3, 2, 1, 1, 3, 6, 10, 12, 12, 10, 6, 3, 1, 1, 4, 10, 20, 31, 40, 44, 40, 31, 20, 10, 4, 1, 1, 5, 15, 35, 65, 101, 135, 155, 155, 135, 101, 65, 35, 15, 5, 1, 1, 6, 21, 56, 120, 216, 336, 456, 546, 580, 546
(list; graph; listen)
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OFFSET
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0,7
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COMMENT
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Coefficient of x^k in (1+x+x^2+x^3)^n is the number of distinct ways in which k unlabeled objects can be distributed in n labeled urns allowing at most 3 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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B. A. Bondarenko, Generalized Pascal Triangles and Pyramids (in Russian), FAN, Tashkent, 1990, ISBN 5-648-00738-8. English translation published by Fibonacci Association, Santa Clara Univ., Santa Clara, CA, 1993; see p. 17.
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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T. D. Noe, Rows n=0..25 of triangle, flattened
S. R. Finch, P. Sebah and Z.-Q. Bai, Odd Entries in Pascal's Trinomial Triangle (arXiv:0802.2654)
W. Florek and T. Lulek, Combinatorial analysis of magnetic configurations
L. Euler, On the expansion of the power of any polynomial (1+x+x^2+x^3+x^4+etc)^n
L. Euler, De evolutione potestatis polynomialis cuiuscunque (1+x+x^2+x^3+x^4+etc)^n E709
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FORMULA
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n-th row is formed by expanding (1+x+x^2+x^3)^n.
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EXAMPLE
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1; 1,1,1,1; 1,2,3,4,3,2,1; 1,3,6,10,12,12,10,6,3,1; ...
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CROSSREFS
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Cf. A007318, A027907.
Sequence in context: A017869 A107469 A167600 this_sequence A017859 A028356 A073791
Adjacent sequences: A008284 A008285 A008286 this_sequence A008288 A008289 A008290
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KEYWORD
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nonn,tabf,easy,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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