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Eigentriangle.
2

%I #12 Dec 11 2019 07:09:58

%S 1,1,1,2,1,2,5,2,2,5,13,5,4,5,14,34,13,10,10,14,41,89,34,26,25,28,41,

%T 122,233,89,68,65,70,82,122,365,610,233,178,170,182,205,244,365,1094,

%U 1597,610,466,445,476,533,610,730,1094,3281

%N Eigentriangle.

%C Left column = odd-indexed Fibonacci numbers prefaced with a 1.

%C Right border = A007051 shifted.

%C Row sums are A007051.

%F Let M = an infinite lower triangular matrix with odd-indexed Fibonacci numbers in every column prefaced with a 1: (1, 1, 2, 5, 13, 34, ...). Q = an infinite lower triangular matrix with A007051 prefaced with a 1 as the main diagonal: (1, 1, 2, 5, 14, 41, 122, 365, 1094, ...); and the rest zeros.

%F A147292 = M * Q

%e First few rows of the triangle =

%e 1;

%e 1, 1;

%e 2, 1, 2;

%e 5, 2, 2, 5;

%e 13, 5, 4, 5, 14;

%e 34, 13, 10, 10, 14, 41;

%e 89, 34, 26, 25, 28, 41, 122;

%e 233, 89, 68, 65, 70, 82, 122, 365;

%e 610, 233, 178, 170, 182, 205, 244, 365, 1094;

%e 1597, 610, 466, 445, 476, 533, 610, 730, 1094, 3281;

%e 4181, 1597, 1220, 1665, 1246, 1394, 1586, 1825, 2188, 3281, 9842;

%e 10946, 4181, 3194, 3050, 3262, 3649, 4148, 4745, 5470, 6562, 9842, 29525;

%e ...

%e Row 4 = (13, 5, 4, 5, 14) = termwise products of (13, 5, 2, 1, 1) and (1, 1, 2, 5, 14).

%K eigen,nonn,tabl

%O 0,4

%A _Gary W. Adamson_, Nov 05 2008