0,2

If Y is a 3-subset of an n-set X then, for n>=4, a(n-4) is the number of 3-subsets of X having at most one element in common with Y. - Milan R. Janjic (agnus(AT)blic.net), Nov 23 2007

The coefficient of x^3 in (1-x-x^2)^{-n} is the coefficient of x^3 in (1+x+2x^2+3x^3)^n. Using the multinomial theorem one then finds that a(n)=n(n+1)(n+8)/3! - Sergio Falcon (sfalcon(AT)dma.ulpgc.es), May 22 2008

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196.

G. E. Bergum and V. E. Hoggatt, Jr., Numerator polynomial coefficient array for the convolved Fibonacci sequence, Fib. Quart., 14 (1976), 43-48.

P. Moree, Convoluted convolved Fibonacci numbers

S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.

S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.

a(n)=n*(n+1)*(n+8)/6. G.f.: x*(3-2*x)/(1-x)^4.

a(n) = A000292(n) + A0002378(n). [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Sep 24 2008]

A006503:=-(-3+2*z)/(z-1)**4; [S. Plouffe in his 1992 dissertation.]

Clear["Global`*"] a[n_] := n(n + 1)(n + 8)/3! Do[Print[n, " ", a[n]], {n, 1, 25}] - Sergio Falcon (sfalcon(AT)dma.ulpgc.es), May 22 2008

a(n) = A095660(n+2, 3): fourth column of (1, 3)-Pascal triangle.

Cf. A000027, A000096, A006504.

Sequence in context: A161672 A122795 A140066 this_sequence A023554 A070880 A027164

Adjacent sequences: A006500 A006501 A006502 this_sequence A006504 A006505 A006506

nonn,easy

N. J. A. Sloane (njas(AT)research.att.com).

Better description from Jeffrey Shallit 8/95.