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%I #15 Apr 02 2022 10:11:56
%S 1,1,1,2,0,1,3,1,0,1,5,1,0,0,1,8,2,1,0,0,1,13,3,1,0,0,0,1,21,5,2,1,0,
%T 0,0,1,34,8,3,2,0,0,0,0,1,55,13,5,2,2,0,0,0,0,1,89,21,8,4,2,1,0,0,0,0,
%U 1,144,34,13,6,4,2,1,0,0,0,0,1,233,55,21,10,5,4,1,1,0,0,0,0,1
%N Triangle read by rows: T(n,k) = T(n-1, k-1) - T(n-k, k-1); with left border = the Fibonacci sequence.
%C Row sums = A137713: (1, 2, 3, 5, 7, 12, 18, 30, 48, 78, 126, ...).
%C A137710 is the analogous triangle with left border = (1, 2, 4, 8, 16, 32, ...).
%H Robert Israel, <a href="/A137712/b137712.txt">Table of n, a(n) for n = 1..10011</a>(rows 1 to 141, flattened)
%F T(n,k) = T(n-1, k-1) - T(n-k, k-1), given left border = (1, 1, 2, 3, 5, 8, 13, ...).
%F Here T(n,k) = T(n-1,k-1) if n-k < k-1. - _Robert Israel_, Aug 20 2018
%e First few rows of the triangle:
%e 1;
%e 1, 1;
%e 2, 0, 1;
%e 3, 1, 0, 1;
%e 5, 1, 0, 0, 1;
%e 8, 2, 1, 0, 0, 1;
%e 13, 3, 1, 0, 0, 0, 1;
%e 21, 5, 2, 1, 0, 0, 0, 1;
%e 34, 8, 3, 2, 0, 0, 0, 0, 1;
%e 55, 13, 5, 2, 2, 0, 0, 0, 0, 1;
%e 89, 21, 8, 4, 2, 1, 0, 0, 0, 0, 1;
%e 144, 34, 13, 6, 4, 2, 1, 0, 0, 0, 0, 1;
%e 233, 55, 21, 10, 5, 4, 1, 1, 0, 0, 0, 0, 1;
%e 377, 89, 34, 16, 8, 5, 4, 1, 1, 0, 0, 0, 0, 1;
%e ...
%p for n from 1 to 20 do
%p T[n,1]:= combinat:-fibonacci(n);
%p for k from 2 to n do
%p if n >= 2*k-1 then T[n,k]:= T[n-1,k-1] - T[n-k,k-1]
%p else T[n,k]:= T[n-1,k-1]
%p fi
%p od:
%p od:
%p seq(seq(T[n,k],k=1..n),n=1..20); # _Robert Israel_, Aug 20 2018
%Y Cf. A137713, A137710.
%K nonn,tabl
%O 1,4
%A _Gary W. Adamson_, Feb 08 2008
%E Corrected by _Robert Israel_, Aug 20 2018
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