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A208515 Triangle of coefficients of polynomials v(n,x) jointly generated with A208514; see the Formula section. 3

%I

%S 1,1,2,1,2,3,1,2,4,5,1,2,5,8,8,1,2,6,11,15,13,1,2,7,14,23,28,21,1,2,8,

%T 17,32,47,51,34,1,2,9,20,42,70,93,92,55,1,2,10,23,53,97,148,181,164,

%U 89,1,2,11,26,65,128,217,306,346,290,144,1,2,12,29,78,163,301

%N Triangle of coefficients of polynomials v(n,x) jointly generated with A208514; see the Formula section.

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

%F v(n,x)=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 1...2

%e 1...2...3

%e 1...2...4...5

%e 1...2...5...8...8

%e First five polynomials v(n,x):

%e 1

%e 1 + 2x

%e 1 + 2x + 3x^2

%e 1 + 2x + 4x^2 + 5x^3

%e 1 + 2x + 5x^2 + 8x^3 + 8x^4

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

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

%t v[n_, x_] := 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[%] (* A208514 *)

%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[%] (* A208515 *)

%Y Cf. A208514.

%K nonn,tabl

%O 1,3

%A _Clark Kimberling_, Feb 28 2012

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Last modified March 8 06:46 EST 2021. Contains 341941 sequences. (Running on oeis4.)