|
%I #10 Mar 30 2024 23:09:10
%S 1,2,1,4,1,1,8,2,1,1,16,4,2,1,1,32,8,3,2,1,1,64,16,6,2,2,1,1,64,16,6,
%T 2,2,1,1,128,32,12,5,2,2,1,1,256,64,24,10,4,2,2,1,1,512,128,48,21,9,4,
%U 2,2,1,1,1024,256,96,42,19,18,4,2,2,1,1,2048,512,192,84,40,18,18,4,2,2,1,1
%N Triangle read by rows: T(n,k) = T(n-1, k-1) - T(n-k, k-1); left border = (1, 2, 4, 8, 16, 32, ...).
%C Row sums = A137711: (1, 3, 6, 12, 24, 47, 92, 183, ...).
%C Eigensequence of the triangle = even-indexed Fibonacci numbers starting (1, 3, 8, 21, 55, ...). Cf. triangle A180339. - _Gary W. Adamson_, Aug 28 2010
%F The triangle is generated by two rules: T(n,k) = T(n-1, k-1) - T(n-k, k-1); and left border = 1, 2, 4, 8, 16, ...
%e First few rows of the triangle:
%e 1;
%e 2, 1;
%e 4, 1, 1;
%e 8, 2, 1, 1;
%e 16, 4, 2, 1, 1;
%e 32, 8, 3, 2, 1, 1;
%e 64, 16, 6, 2, 2, 1, 1;
%e 128, 32, 12, 5, 2, 2, 1, 1;
%e 256, 64, 24, 10, 4, 2, 2, 1, 1;
%e 512, 128, 48, 21, 9, 4, 2, 2, 1, 1;
%e ...
%Y Cf. A137711.
%Y Cf. A180339. - _Gary W. Adamson_, Aug 28 2010
%K nonn,tabl
%O 1,2
%A _Gary W. Adamson_, Feb 08 2008
|
