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 A209702 Triangle of coefficients of polynomials v(n,x) jointly generated with A209701; see the Formula section. 3

%I #5 Mar 30 2012 18:58:15

%S 1,2,3,3,5,7,4,8,16,17,5,12,30,47,41,6,17,50,99,134,99,7,23,77,181,

%T 315,373,239,8,30,112,302,628,968,1020,577,9,38,156,472,1128,2090,

%U 2898,2751,1393,10,47,210,702,1882,4020,6738,8495,7338,3363,11,57

%N Triangle of coefficients of polynomials v(n,x) jointly generated with A209701; see the Formula section.

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

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

%F v(n,x)=2x*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 2...3

%e 3...5....7

%e 4...8....16...17

%e 5...12...30...57...41

%e First three polynomials v(n,x): 1, 2 + 3x , 3 + 5x + 7x^2.

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

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

%t v[n_, x_] := 2 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[%] (* A209701 *)

%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[%] (* A209702 *)

%Y Cf. A209701, A208510.

%K nonn,tabl

%O 1,2

%A _Clark Kimberling_, Mar 12 2012

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Last modified August 6 04:41 EDT 2024. Contains 374957 sequences. (Running on oeis4.)