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 A210741 Triangle of coefficients of polynomials u(n,x) jointly generated with A210742; see the Formula section. 3

%I

%S 1,1,3,1,5,8,1,7,19,21,1,9,34,65,55,1,11,53,141,210,144,1,13,76,257,

%T 534,654,377,1,15,103,421,1111,1905,1985,987,1,17,134,641,2041,4447,

%U 6512,5911,2584,1,19,169,925,3440,9038,16837,21557,17345,6765,1

%N Triangle of coefficients of polynomials u(n,x) jointly generated with A210742; see the Formula section.

%C Rows end with even-indexed Fibonacci numbers

%C Row sums: A007070

%C Alternating row sums: signed powers of 2

%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+1)*v(n-1,x)+1,

%F where u(1,x)=1, v(1,x)=1.

%e First five rows:

%e 1

%e 1...3

%e 1...5...8

%e 1...7...19...21

%e 1...9...34...65...55

%e First three polynomials u(n,x): 1, 1+ 3x, 1 + 5x + 8x^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 + 1)*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[%] (* A210741 *)

%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[%] (* A210742 *)

%Y Cf. A210742, A208510.

%K nonn,tabl

%O 1,3

%A _Clark Kimberling_, Mar 24 2012

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Last modified January 23 15:15 EST 2021. Contains 340385 sequences. (Running on oeis4.)