%I
%S 1,1,1,1,2,2,1,4,4,4,1,7,10,8,8,1,12,24,20,16,16,1,20,52,56,40,32,32,
%T 1,33,112,144,112,80,64,64,1,54,238,344,320,224,160,128,128,1,88,496,
%U 828,848,640,448,320,256,256
%N Triangle, by rows, generated from the INVERT transforms of (1, 1, 2, 4, 8, 16, ...).
%C Row sums = A001519, the oddindexed Fibonacci terms. The triangle is a companion to A213947, having row sums of the evenindexed Fibonacci terms.
%F Create an array in which the nth row is the INVERT transform of the first n terms in the sequence (1, 1, 2, 4, 8, 16, 32, ...):
%F 1, 1, 1, 1, 1, 1,
%F 1, 2, 3, 5, 8, 13, (essentially A000045)
%F 1, 2, 5, 9, 18, 37, (essentially A077947)
%F 1, 2, 5, 13, 26, 57,
%F Terms of the nth row of the triangle are the finite differences downwards the nth column of this array.
%e First few rows of the triangle are:
%e 1;
%e 1, 1;
%e 1, 2, 2;
%e 1, 4, 4, 4;
%e 1, 7, 20, 8, 8;
%e 1, 12, 24, 20, 16, 16;
%e 1, 20, 52, 56, 40, 32, 32;
%e 1, 33, 112, 144, 112, 80, 64, 64;
%e 1, 54, 238, 344, 320, 224, 160, 128, 128;
%e 1, 88, 496, 828, 848, 640, 448, 320, 256, 256;
%e ...
%p read("transforms") ;
%p A213948i := proc(n,k)
%p if n = 1 then
%p L := [1,seq(0,i=0..k)] ;
%p else
%p L := [1,seq(2^i,i=0..n2),seq(0,i=0..k)] ;
%p end if;
%p INVERT(L) ;
%p op(k,%) ;
%p end proc:
%p A213948 := proc(n,k)
%p if k = 1 then
%p 1;
%p else
%p A213948i(k,n)A213948i(k1,n) ;
%p end if;
%p end proc: # _R. J. Mathar_, Jun 30 2012
%Y Cf. A001519, A213947, A000071 (2nd column), A020714 (subdiagonal), A005009 (subdiagonal).
%K nonn,tabl,changed
%O 1,5
%A _Gary W. Adamson_, Jun 25 2012
