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A210188 Triangle of coefficients of polynomials v(n,x) jointly generated with A210187; see the Formula section. 3

%I

%S 1,2,2,3,7,2,4,16,11,2,5,30,36,15,2,6,50,91,64,19,2,7,77,196,204,100,

%T 23,2,8,112,378,540,385,144,27,2,9,156,672,1254,1210,650,196,31,2,10,

%U 210,1122,2640,3289,2366,1015,256,35,2,11,275,1782,5148,8008

%N Triangle of coefficients of polynomials v(n,x) jointly generated with A210187; see the Formula section.

%C Row sums: -1+(odd-indexed Fibonacci numbers): 1,4,12,...

%C Period of alternating row sums: (1,-,-2,-3,-2,0)

%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)=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 2...2

%e 3...7....2

%e 4...16...11...2

%e 5...30...36...15...2

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

%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_] := 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[%] (* A210187 *)

%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[%] (* A210188 *)

%Y Cf. A210187, A208510.

%K nonn,tabl

%O 1,2

%A _Clark Kimberling_, Mar 18 2012

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Last modified November 16 20:05 EST 2019. Contains 329203 sequences. (Running on oeis4.)