OFFSET
0,3
COMMENTS
For n >=0 the sequence contains the triangular numbers; for n >= 5 have to add the tetrahedral numbers; for n >= 10 have to add the numbers binomial(n,4) (starting with 0,1,5,...); for n >= 15 have to add the numbers binomial(n,5) (starting with 0,1,6,..); in general, for n >= 5*k have to add to the sequence the numbers binomial(n, k+2), k >= 0.
For example, a(19) = 190+560+495+56, where 190 is a triangular number, 560 is a tetrahedral number, 495 is a number binomial(n,4) and 56 is a number binomial(m,5) (with the proper n, m due to shifts in the names of the sequences).
First difference is A099559.
FORMULA
Conjectures from Colin Barker, May 17 2020: (Start)
G.f.: x / ((1 - x)^2*(1 - x + x^2)*(1 - x^2 - x^3)).
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) + a(n-5) - 2*a(n-6) + a(n-7) for n>6.
(End)
EXAMPLE
For example, for n=11, a(6) = 22 and the sets are: {1,6}, {1,7}, {1,8}, {1,9}, {1,10}, {1,11}, {2,7}, {2,8}, {2,9}, {2,10}, {2,11}, {3,8}, {3,9}, {3,10}, {3,11}, {4,9}, {4,10}, {4,11}, {5,10}, {5,11}, {6,11}, {1,6,11}.
CROSSREFS
KEYWORD
nonn
AUTHOR
Enrique Navarrete, May 01 2020
STATUS
approved