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%I #7 May 01 2013 21:06:46
%S 1,1,1,1,0,1,1,1,1,1,1,1,2,1,1,1,2,3,3,2,1,1,3,5,5,5,3,1,1,5,8,9,9,8,
%T 5,1,1,8,13,15,16,15,13,8,1,1,13,21,25,27,27,25,21,13,1,1,21,34,41,45,
%U 46,45,41,34,21,1
%N Triangle read by rows based on the Fibonacci sequence A000045: t(n,m) = 1 + Fibonacci[n] - Fibonacci[m] - Fibonacci[n - m].
%C Row sums are {1, 2, 2, 4, 6, 12, 23, 46, 90, 174, 330,...} (see A188538).
%C More generally, we can define for a sequence with a(n)=0 : add one;
%C t(n,m)=1+a(n)-a(m)-a(n-m)
%C or a(0)=1: add two:
%C t(n,m)=2+a(n)-a(m)-a(n-m).
%F t(n,m)=1 + Fibonacci[n] - Fibonacci[m] - Fibonacci[n - m].
%e {1},
%e {1, 1},
%e {1, 0, 1},
%e {1, 1, 1, 1},
%e {1, 1, 2, 1, 1},
%e {1, 2, 3, 3, 2, 1},
%e {1, 3, 5, 5, 5, 3, 1},
%e {1, 5, 8, 9, 9, 8, 5, 1},
%e {1, 8, 13, 15, 16, 15, 13, 8, 1},
%e {1, 13, 21, 25, 27, 27, 25, 21, 13, 1},
%e {1, 21, 34, 41, 45, 46, 45, 41, 34, 21, 1}
%t t[n_, m_] = 1 + Fibonacci[n] - Fibonacci[m] - Fibonacci[n - m];
%t Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}];
%t Flatten[%]
%Y Cf. A000045, A188538.
%K nonn,tabl
%O 0,13
%A _Roger L. Bagula_, Feb 03 2009
%E Edited by _N. J. A. Sloane_, Apr 03 2011
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