A131131 - OEIS

%I #10 Jan 25 2020 18:12:23

%S 1,1,1,4,5,1,4,12,9,1,4,16,24,13,1,4,20,40,40,17,1,4,24,60,80,60,21,1,

%T 4,28,84,140,140,84,25,1,4,32,112,224,280,224,112,29,1

%N 4*A007318 - 3*A097806.

%C Row sums = A131130, (1, 2, 10, 26, 52, 98, 190, ...), the binomial transform of (1, 1, 7, 1, 7, 1, ...). Generally, triangles generated from N*A007318 - (N-1)*A097806 have row sums that are binomial transforms of (1, 1, (N-1), 1, (N-1), 1, ...). A095121 = (1, 2, 6, 14, 30, 62, ...), the binomial transform of (1, 1, 3, 1, 3, 1, ...) and = row sums of A131108.

%C Triangle T(n,k), 0 <= k <= n,read by rows given by [1,3,-4,1,0,0,0,0,0,0,0,...] DELTA [1,0,0,1,0,0,0,0,0,0,0,...] where DELTA is the operator defined in A084938. - _Philippe Deléham_, Dec 18 2007

%F 4*A007318 - 3*A097806, where A007318 = Pascal's triangle and A097806 = the pairwise operator.

%F G.f.: (1-x*y+3*x^2+3*x^2*y)/((-1+x+x*y)*(x*y-1)). - _R. J. Mathar_, Aug 12 2015

%e First few rows of the triangle:

%e   1;

%e   1,  1;

%e   4,  5,  1;

%e   4, 12,  9,  1;

%e   4, 16, 24, 13,  1

%e   4, 20, 40, 40, 17,  1;

%e   ...

%Y Cf. A131130, A131129, A131128, A131127, A046055, A131108, A095121, A097806.

%K nonn,tabl

%O 0,4

%A _Gary W. Adamson_, Jun 16 2007