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A209694 Triangle of coefficients of polynomials v(n,x) jointly generated with A209693; see the Formula section. 3

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

%S 1,3,1,4,6,1,5,13,10,1,6,22,32,15,1,7,33,71,66,21,1,8,46,131,186,121,

%T 28,1,9,61,216,415,422,204,36,1,10,78,330,801,1121,862,323,45,1,11,97,

%U 477,1400,2507,2689,1625,487,55,1,12,118,661,2276,4977,6902

%N Triangle of coefficients of polynomials v(n,x) jointly generated with A209693; see the Formula section.

%C Alternating row sums are periodic. 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)=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 3...1

%e 4...6....1

%e 5...13...10...1

%e 6...22...32...15...1

%e First three polynomials v(n,x): 1, 3 + x , 4 + 6x + x^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_] := 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[%] (* A209693 *)

%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[%] (* A209694 *)

%Y Cf. A209693, A208510.

%K nonn,tabl

%O 1,2

%A _Clark Kimberling_, Mar 12 2012

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Last modified March 28 13:42 EDT 2024. Contains 371254 sequences. (Running on oeis4.)