OFFSET
0,2
COMMENTS
Also the first occurring nonzero terms in rows of triangle A261897, without repetitions. - Reinhard Zumkeller, Sep 06 2015
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..200
L. Haddad and C. Helou, Finite Sequences Dominated by the Squares, Journal of Integer Sequences, Volume 18, 2015, Issue 1, Article 15.1.8.
FORMULA
a(n) = Sum_{k=1..n} (-1)^{k-1}* C((n-k+1)^2+k-1,k) * a(n-k), for n>1.
a(n) = C(n^2,n-1) + C(n^2-1,n-1) - Sum_{k=2..n-1} C(n^2-k^2,n-k+1) *a(k-1), for n>1.
Conjecture: lim n->infinity a(n)^(1/n)/n = 2. - Vaclav Kotesovec, Feb 26 2017
EXAMPLE
For n=2 the a(2) = 7 solutions are (0,1), (0,2), (0,3), (0,4), (1,2), (1,3), (1,4).
MAPLE
a:= proc(n) option remember; `if`(n<2, n+1, add((-1)^(k-1)*
binomial((n-k+1)^2+k-1, k) * a(n-k), k=1..n))
end:
seq(a(n), n=0..25); # Alois P. Heinz, Aug 15 2014
MATHEMATICA
a[0] = 1; a[1] = 2; a[n_] := a[n] = Sum[(-1)^(k-1)*Binomial[(n-k+1)^2+k-1, k]*a[n-k], {k, 1, n}]; Table[a[n], {n, 0, 25}] (* Jean-François Alcover, Feb 26 2017 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Charles Helou, Aug 14 2014
STATUS
approved