OFFSET
0,3
COMMENTS
If Y is a 3-subset of an n-set X then, for n >= 4, a(n-3) is the number of 4-subsets of X which have neither one element nor two elements in common with Y; a(n-3) is then also the number of (n-4)-subsets of X which have neither one element nor two elements in common with Y. - Milan Janjic, Dec 28 2007
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
FORMULA
a(n) = (n^4 - 6*n^3 + 11*n^2 + 18*n)/24.
From Paul Barry, Sep 23 2004: (Start)
Binomial transform of (0, 1, 0, 0, 1, 0, 0, 0, ...), or g.f. x+x^4.
G.f.: x*(1-3*x+3*x^2)/(1-x)^5;
a(n) = C(n,1) + C(n,4). (End)
E.g.f.: x*(24 + x^3)*exp(x)/24. - G. C. Greubel, Nov 08 2018
MATHEMATICA
Table[(n^4 -6*n^3 +11*n^2 +18*n)/24, {n, 0, 50}] (* G. C. Greubel, Nov 08 2018 *)
PROG
(Magma) [(n^4-6*n^3+11*n^2-6*n)/24 +n: n in [0..50]]; // Vincenzo Librandi, Aug 21 2011
(PARI) vector(50, n, n--; (n^4 -6*n^3 +11*n^2 +18*n)/24) \\ G. C. Greubel, Nov 08 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
Corrected and extended by Erich Friedman
STATUS
approved