login
Diagonal sums of number triangle A108359.
2

%I #14 Jun 13 2015 00:51:50

%S 1,1,2,4,7,13,25,47,90,172,329,629,1202,2294,4374,8330,15847,30115,

%T 57172,108434,205473,389019,735927,1391121,2627720,4960134,9356707,

%U 17639323,33234036,62580444,117776828,221542596,416524573,782743029

%N Diagonal sums of number triangle A108359.

%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (3,0,-4,-2,2,4,0,-1,-1).

%F a(n) = sum{k=0..floor(n/2)} ( sum{j=0..n-2k} C(k, j) * C(n-k-j, k) * floor((j+2)/2) ).

%F Empirical g.f.: (x^2+x-1)^2 / ((x-1)^2*(x+1)*(x^3+x^2+x-1)^2). - _Colin Barker_, Sep 26 2014

%p A108361:=n->add(add(binomial(k,j)*binomial(n-k-j,k)*floor((j+2)/2),j=0..n-2*k),k=0..floor(n/2)): seq(A108361(n), n=0..50); # _Wesley Ivan Hurt_, Sep 26 2014

%t Table[Sum[Sum[Binomial[k, j] Binomial[n - k - j, k] Floor[(j + 2)/2], {j, 0, n - 2 k}], {k, 0, Floor[n/2]}], {n, 0, 30}] (* _Wesley Ivan Hurt_, Sep 26 2014 *)

%Y Cf. A108359.

%K easy,nonn

%O 0,3

%A _Paul Barry_, May 31 2005