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A210033 Triangle of coefficients of polynomials u(n,x) jointly generated with A210034; see the Formula section. 3

%I

%S 1,3,6,1,11,3,1,19,8,3,1,32,18,9,3,1,53,38,22,10,3,1,87,76,51,26,11,3,

%T 1,142,147,111,65,30,12,3,1,231,277,233,151,80,34,13,3,1,375,512,474,

%U 338,196,96,38,14,3,1,608,932,942,730,463,246,113,42,15,3,1

%N Triangle of coefficients of polynomials u(n,x) jointly generated with A210034; see the Formula section.

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

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

%F v(n,x)=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 3

%e 6....1

%e 11...3...1

%e 19...8...3...1

%e First three polynomials u(n,x): 1, 3, 6 + x.

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

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

%t v[n_, x_] := 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[%] (* A210033 *)

%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[%] (* A210034 *)

%Y Cf. A210034, A208510.

%K nonn,tabf

%O 1,2

%A _Clark Kimberling_, Mar 16 2012

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Last modified November 17 06:06 EST 2019. Contains 329217 sequences. (Running on oeis4.)