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A210740 Triangle of coefficients of polynomials v(n,x) jointly generated with A210739; see the Formula section. 3

%I

%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

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Last modified October 19 03:34 EDT 2019. Contains 328211 sequences. (Running on oeis4.)