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A210551 Triangle of coefficients of polynomials v(n,x) jointly generated with A172431; see the Formula section. 2

%I

%S 1,3,1,5,6,1,7,15,10,1,9,28,35,15,1,11,45,84,70,21,1,13,66,165,210,

%T 126,28,1,15,91,286,495,462,210,36,1,17,120,455,1001,1287,924,330,45,

%U 1,19,153,680,1820,3003,3003,1716,495,55,1,21,190,969,3060,6188

%N Triangle of coefficients of polynomials v(n,x) jointly generated with A172431; see the Formula section.

%C Row sums: -1+odd-indexed Fibonacci numbers

%C Alternating row sums: 1,2,0,1,2,0,1,2,0,...

%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)+1,

%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 1...2

%e 1...3...4

%e 1...3...9....8

%e 1...3...10...25...16

%e First three polynomials v(n,x): 1, 1 + 2x , 1 + 3x + 4x^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] + 1;

%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[%] (* A172431 *)

%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[%] (* A210551 *)

%Y Cf. A172431, A208510.

%K nonn,tabl

%O 1,2

%A _Clark Kimberling_, Mar 22 2012

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Last modified November 19 16:06 EST 2019. Contains 329320 sequences. (Running on oeis4.)