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

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.

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: A058077 A122795 A140066 this_sequence A023554 A070880 A027164

Adjacent sequences: A006500 A006501 A006502 this_sequence A006504 A006505 A006506

nonn,easy

njas

Better description from Jeffrey Shallit 8/95.