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%I #15 Dec 11 2019 09:49:04
%S 1,1,1,2,1,2,4,2,2,5,8,4,4,5,13,16,8,8,10,13,34,32,16,16,20,26,34,89,
%T 64,32,32,40,52,68,89,233,128,64,64,80,104,136,178,233,610
%N Eigentriangle, row sums = A001519, odd-indexed Fibonacci numbers.
%C Row sums = A001519, the odd-indexed Fibonacci numbers starting (1, 2, 5, 13, 34, ...).
%C Sum of n-th row terms = rightmost term of next row.
%F Triangle read by rows, M*Q. M = an infinite lower triangular matrix with (1, 1, 2, 4, 8, 16, ...) in every column and Q = a matrix (1, 1, 2, 5, 13, 34, ...) as the main diagonal and the rest zeros.
%F Let M = production matrix for reversed rows of the triangle as follows:
%F 1, 1;
%F 1, 0, 2;
%F 1, 0, 0, 2;
%F 1, 0, 0, 0, 2;
%F 1, 0, 0, 0, 0, 2;
%F ...
%F Reversal of n-th row of triangle A152251 = top row terms of M^(n-1). Example: top row of M^3 = (5, 2, 2, 4). - _Gary W. Adamson_, Jul 07 2011
%e First few rows of the triangle =
%e 1;
%e 1, 1;
%e 2, 1, 2;
%e 4, 2, 2, 5;
%e 8, 4, 4, 5, 13;
%e 16, 8, 8, 10, 13, 34;
%e 32, 16, 16, 20, 26, 34, 89;
%e 64, 32, 32, 40, 52, 68, 89, 233;
%e 128, 64, 64, 80, 104, 136, 178, 233, 610;
%e ...
%e Row 4 = (8, 4, 4, 5, 13) = termwise products of (8, 4, 2, 1, 1) and (1, 1, 2, 5, 13).
%Y Cf. A001519.
%K eigen,nonn,tabl
%O 1,4
%A _Gary W. Adamson_, Nov 30 2008
%E Last term corrected by _Olivier Gérard_, Aug 11 2016
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