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%I #10 Jan 02 2016 14:04:50
%S 1,2,2,3,4,4,5,8,8,8,8,16,20,16,16,13,30,44,48,32,32,21,56,92,112,112,
%T 64,64,34,102,188,256,272,256,128,128,55,184,372,560,672,640,576,256,
%U 256,89,328,724,1184,1552,1696,1472,1280,512,512,144,580,1384
%N Triangle of coefficients of polynomials v(n,x) jointly generated with A207612; see Formula section.
%C Only column 1 contains odd numbers.
%C column 1: A000045 (Fibonacci sequence)
%C row sums: A002878 (bisection of Lucas sequence)
%C top edge: A000079 (powers of 2)
%F u(n,x) = u(n-1,x) + v(n-1,x), v(n,x) = u(n-1,x) + 2x*v(n-1,x) + 1, where u(1,x) = 1, v(1,x) = 1.
%F With offset 0, the Riordan array ((1 + z)/(1 - z - z^2), 2*z*(1 - z)/(1 - z - z^2)) with o.g.f. (1 + z)/(1 - z - z^2 - x*(2*z - 2*z^2)) = 1 + (2 + 2*x)*z + (3 + 4*x + 4*x^2)*z^2 + .... - _Peter Bala_, Dec 30 2015
%e First five rows:
%e 1
%e 2 2
%e 3 4 4
%e 5 8 8 8
%e 8 16 20 16 16
%t u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t u[n_, x_] := u[n - 1, x] + v[n - 1, x]
%t v[n_, x_] := u[n - 1, x] + 2 x*v[n - 1, x] + 1
%t Table[Factor[u[n, x]], {n, 1, z}]
%t Table[Factor[v[n, x]], {n, 1, z}]
%t cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t TableForm[cu]
%t Flatten[%] (* A207612 *)
%t Table[Expand[v[n, x]], {n, 1, z}]
%t cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t TableForm[cv]
%t Flatten[%] (* A207613 *)
%Y A000045 (column 1), A000079 (main diagonal), A002878 (row sums). Cf. A207612, A208510.
%K nonn,tabl,easy
%O 1,2
%A _Clark Kimberling_, Feb 19 2012
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