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%I #5 Feb 11 2014 05:14:54
%S 1,1,2,2,2,3,3,5,3,4,5,8,9,4,5,8,15,15,14,5,6,13,26,31,24,20,6,7,21,
%T 46,57,54,35,27,7,8,34,80,108,104,85,48,35,8,9,55,139,199,209,170,125,
%U 63,44,9,10,89,240,366,404,360,258,175,80,54,10,11
%N Triangle T(i,j) read by rows: T(i,1) = Fibonacci(i) for all i; T(i,i) = i for all i; T(i,j) = T(i-1,j) + T(i-2,j) + T(i-1,j-1) - T(i-2,j-1).
%C Sum of n-th row terms = (2^n - 1) (see solution in Fibonacci Quarterly).
%H Jyoti P. Shiwalker and M. N. Despande, <a href="http://www.fq.math.ca/Problems/elementary45-2.pdf">Problem B-1033</a>, Fibonacci Quarterly, Vol. 45, Number 2; 2007; p. 181.
%H Russ Euler and Jawad Sadek, editors, <a href="http://www.fq.math.ca/Problems/November2007elementary.pdf">Elementary Problems and Solutions</a>, Fibonacci Quarterly, Vol. 45, Number 4; 2007; p. 181.
%e First few rows of the triangle are:
%e 1;
%e 1, 2;
%e 2, 2, 3;
%e 3, 5, 3, 4;
%e 5, 8, 9, 4, 5;
%e 8, 15, 15, 14, 5, 6;
%e 13, 26, 31, 24, 20, 6, 7;
%e 21, 46, 57, 54, 5, 27, 7, 8;
%e ...
%o (PARI) t(i, j) = {if ((i <= 0) || (j <= 0), 0, if (j == 1, fibonacci(i), if (i == j, i, t(i-1,j) + t(i-2,j) + t(i-1,j-1) - t(i-2,j-1););););}
%o tabl(nn) = {for (n=1, nn, for (k=1, n, print1(t(n, k), ", ");););} \\ _Michel Marcus_, Feb 11 2014
%K nonn,tabl
%O 1,3
%A _Gary W. Adamson_, May 01 2008
%E More terms from _Michel Marcus_, Feb 11 2014
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