cp's OEIS Frontend

A058393 A square array based on 1^n (A000012) with each term being the sum of 2 consecutive terms in the previous row.

%I A058393 #3 Mar 30 2012 18:51:32
%S A058393 1,0,1,1,1,1,0,1,2,1,1,1,2,3,1,0,1,2,4,4,1,1,1,2,4,7,5,1,0,1,2,4,8,11,
%T A058393 6,1,1,1,2,4,8,15,16,7,1,0,1,2,4,8,16,26,22,8,1,1,1,2,4,8,16,31,42,29,
%U A058393 9,1,0,1,2,4,8,16,32,57,64,37,10,1,1,1,2,4,8,16,32,63,99,93,46,11,1,0
%N A058393 A square array based on 1^n (A000012) with each term being the sum of 2 consecutive terms in the previous row.
%C A058393 Changing the formula by replacing T(0,2n)=T(1,n) by T(0,2n)=T(m,n) for some other value of m, would make the generating function change to coefficient of x^n in expansion of (1+x)^k/(1-x^2)^m. This would produce A058394, A058395, A057884, (and effectively A007318).
%F A058393 T(n, k)=T(n-1, k-1)+T(n, k-1) with T(0, k)=1, T(1, 1)=1, T(0, 2n)=T(1, n) and T(0, 2n+1)=0. Coefficient of x^n in expansion of (1+x)^k/(1-x^2).
%e A058393 Rows are (1,0,1,0,1,0,1,...), (1,1,1,1,1,1,...), (1,2,2,2,2,2,...), (1,3,4,4,4,...) etc.
%Y A058393 Rows are A000035 (A000012 with zeros), A000012, A040000 etc. Columns are A000012, A001477, A000124, A000125, A000127, A006261, A008859, A008860, A008861, A008862, A008863 etc. Diagonals include A000079, A000225, A000295, A002662, A002663, A002664, A035038, A035039, A035040, A035041, etc. The triangles A008949, A054143 and A055248 also appear in the half of the array which is not powers of 2.
%K A058393 nonn,tabl
%O A058393 0,9
%A A058393 _Henry Bottomley_, Nov 24 2000