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 A152251 Eigentriangle, row sums = A001519, odd-indexed Fibonacci numbers. 2

%I

%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 GĂ©rard_, Aug 11 2016

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Last modified July 27 18:27 EDT 2021. Contains 346308 sequences. (Running on oeis4.)