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A210740 Triangle of coefficients of polynomials v(n,x) jointly generated with A210739; see the Formula section.

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