Search: id:A008287
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%I A008287
%S A008287 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,
%T A008287 40,31,20,10,4,1,1,5,15,35,65,101,135,155,155,135,101,65,35,15,5,1,
%U A008287 1,6,21,56,120,216,336,456,546,580,546
%N A008287 Triangle of quadrinomial coefficients.
%C A008287 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
%D A008287 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.
%D A008287 L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 78.
%D A008287 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).
%D A008287 Freund, J. E., Restricted Occupancy Theory - A Generalization of Pascal's 
               Triangle, American Mathematical Monthly, Vol. 63, No. 1 (1956), pp. 
               20-27.
%H A008287 T. D. Noe, <a href="b008287.txt">Rows n=0..25 of triangle, flattened</
               a>
%H A008287 S. R. Finch, P. Sebah and Z.-Q. Bai, <a href="http://arXiv.org/abs/0802.2654">
               Odd Entries in Pascal's Trinomial Triangle</a> (arXiv:0802.2654)
%H A008287 W. Florek and T. Lulek, <a href="http://www.mat.univie.ac.at/~slc/opapers/
               s26florek.html">Combinatorial analysis of magnetic configurations</
               a>
%H A008287 L. Euler, <a href="http://arXiv.org/abs/math.HO/0505425">On the expansion 
               of the power of any polynomial (1+x+x^2+x^3+x^4+etc)^n</a>
%H A008287 L. Euler, <a href="http://www.eulerarchive.org">De evolutione potestatis 
               polynomialis cuiuscunque (1+x+x^2+x^3+x^4+etc)^n</a> E709
%F A008287 n-th row is formed by expanding (1+x+x^2+x^3)^n.
%e A008287 1; 1,1,1,1; 1,2,3,4,3,2,1; 1,3,6,10,12,12,10,6,3,1; ...
%Y A008287 Cf. A007318, A027907.
%Y A008287 Sequence in context: A017869 A107469 A167600 this_sequence A017859 A028356 
               A073791
%Y A008287 Adjacent sequences: A008284 A008285 A008286 this_sequence A008288 A008289 
               A008290
%K A008287 nonn,tabf,easy,nice
%O A008287 0,7
%A A008287 N. J. A. Sloane (njas(AT)research.att.com).

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