0,7

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

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.

T. D. Noe, Rows n=0..25 of triangle, flattened

S. 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

n-th row is formed by expanding (1+x+x^2+x^3)^n.

1; 1,1,1,1; 1,2,3,4,3,2,1; 1,3,6,10,12,12,10,6,3,1; ...

Cf. A007318, A027907.

Sequence in context: A017879 A017869 A107469 this_sequence A017859 A028356 A073791

Adjacent sequences: A008284 A008285 A008286 this_sequence A008288 A008289 A008290

nonn,tabf,easy,nice

njas