%I A115284
%S A115284 1,3,3,4,10,4,4,15,15,4,4,16,26,16,4,4,16,31,31,16,4,4,16,32,42,32,16,
               4,
%T A115284 4,16,32,47,47,32,16,4,4,16,32,48,58,48,32,16,4,4,16,32,48,63,63,48,32,
%U A115284 16,4,4,16,32,48,64,74,64,48,32,16,4
%N A115284 Correlation triangle of 4-C(1,n)-2*C(0,n) (A113311).
%C A115284 Row sums are the coordination sequence for cubic lattice A005899. Diagonal 
               sums are A115285. T(2n,n) is A113770. T(2n,n)-T(2n,n+1) is 1,6,10,
               10,10,.... (10-4C(1,n)-5C(0,n)).
%F A115284 G.f.: (1+x)^2*(1+x*y)^2/((1-x)(1-x*y)(1-x^2*y)); Number triangle T(n, 
               k)=sum{j=0..n, [j<=k]*(4-C(1, k-j)-2C(0, k-j))*[j<=n-k]*((4-C(1, 
               n-k-j)-2C(0, n-k-j))}.
%e A115284 Triangle begins
%e A115284 1;
%e A115284 3, 3;
%e A115284 4, 10, 4;
%e A115284 4, 15, 15, 4;
%e A115284 4, 16, 26, 16, 4;
%e A115284 4, 16, 31, 31, 16, 4;
%e A115284 4, 16, 32, 42, 32, 16, 4;
%Y A115284 Sequence in context: A107635 A132319 A130626 this_sequence A144626 A033707 
               A049925
%Y A115284 Adjacent sequences: A115281 A115282 A115283 this_sequence A115285 A115286 
               A115287
%K A115284 easy,nonn,tabl
%O A115284 0,2
%A A115284 Paul Barry (pbarry(AT)wit.ie), Jan 19 2006