|
%I #10 Nov 09 2013 03:44:18
%S 1,2,2,2,6,5,2,7,18,13,2,7,25,53,34,2,7,26,86,154,89,2,7,26,96,286,
%T 443,233,2,7,26,97,348,926,1264,610,2,7,26,97,361,1234,2935,3582,1597,
%U 2,7,26,97,362,1334,4280,9143,10092,4181,2,7,26,97,362,1350,4875
%N Triangle of coefficients of polynomials v(n,x) jointly generated with A210739; see the Formula section.
%C Row n ends with odd-indexed Fibonacci numbers.
%C Limiting row: A001075.
%C Row sums: A003462.
%C Alternating row sums: 1,0,1,0,1,0,1,0,1,0,...
%C For a discussion and guide to related arrays, see A208510.
%F u(n,x) = 2x*u(n-1,x) + x*v(n-1,x) + 1,
%F v(n,x) = (x+1)*u(n-1,x) + x*v(n-1,x) + 1,
%F where u(1,x)=1, v(1,x)=1.
%e First five rows:
%e 1
%e 2...2
%e 2...6...5
%e 2...7...18...13
%e 2...7...25...53...34
%e First three polynomials v(n,x): 1, 2 + 2x, 2 + 6x + 5x^2
%t u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t u[n_, x_] := 2 x*u[n - 1, x] + x*v[n - 1, x] + 1;
%t v[n_, x_] := (x + 1)*u[n - 1, x] + x*v[n - 1, x] + 1;
%t Table[Expand[u[n, x]], {n, 1, z/2}]
%t Table[Expand[v[n, x]], {n, 1, z/2}]
%t cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t TableForm[cu]
%t Flatten[%] (* A210739 *)
%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[%] (* A210740 *)
%Y Cf. A210739, A208510.
%K nonn,tabl
%O 1,2
%A _Clark Kimberling_, Mar 24 2012
|
