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A209761 Triangle of coefficients of polynomials u(n,x) jointly generated with A209762; see the Formula section. 3

%I #7 Mar 30 2012 18:58:15

%S 1,1,2,2,5,4,3,10,14,8,4,17,34,36,16,5,26,68,104,88,32,6,37,120,240,

%T 296,208,64,7,50,194,480,776,800,480,128,8,65,294,868,1736,2352,2080,

%U 1088,256,9,82,424,1456,3472,5824,6784,5248,2432,512,10,101,588

%N Triangle of coefficients of polynomials u(n,x) jointly generated with A209762; see the Formula section.

%C Column 1: 1,1,2,3,4,5,6,7,...

%C Column 2: 1+1, 1+2^2, 1+3^2, 1+4^2,...

%C Last term in row n: 2^(n-1)

%C Alternating row sums: 1,-1,1,-1,1,-1,1,-1,...; A033999

%C For a discussion and guide to related arrays, see A208510.

%F u(n,x)=x*u(n-1,x)+(x+1)*v(n-1,x),

%F v(n,x)=x*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...2

%e 2...5....4

%e 3...10...14...8

%e 4...17...34...36...16

%e First three polynomials u(n,x): 1, 1 + 2x, 2 + 5x + 4x^2.

%t u[1, x_] := 1; v[1, x_] := 1; z = 16;

%t u[n_, x_] := x*u[n - 1, x] + (x + 1)*v[n - 1, x];

%t v[n_, x_] := x*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[%] (* A209761 *)

%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[%] (* A209762 *)

%Y Cf. A209762, A208510.

%K nonn,tabl

%O 1,3

%A _Clark Kimberling_, Mar 14 2012

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Last modified March 28 12:26 EDT 2024. Contains 371254 sequences. (Running on oeis4.)