cp's OEIS Frontend

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

%I A210551 #25 May 18 2020 06:17:16
%S A210551 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 A210551 126,28,1,15,91,286,495,462,210,36,1,17,120,455,1001,1287,924,330,45,
%U A210551 1,19,153,680,1820,3003,3003,1716,495,55,1,21,190,969,3060,6188
%N A210551 Triangle of coefficients of polynomials v(n,x) jointly generated with A172431; see the Formula section.
%C A210551 Row sums: -1+odd-indexed Fibonacci numbers
%C A210551 Alternating row sums: 1,2,0,1,2,0,1,2,0,...
%C A210551 For a discussion and guide to related arrays, see A208510.
%F A210551 u(n,x)=x*u(n-1,x)+x*v(n-1,x)+1,
%F A210551 v(n,x)=u(n-1,x)+(x+1)*v(n-1,x)+1
%F A210551 where u(1,x)=1, v(1,x)=1.
%e A210551 From _Paul Weisenhorn_, May 17 2020 : (Start)
%e A210551 First five rows of v(n.x):
%e A210551   1
%e A210551   3   1
%e A210551   5   6   1
%e A210551   7  15  10   1
%e A210551   9  28  35  15  1
%e A210551 First three polynomials v(n,x): 1, 3 + x, 5 + 6x + x^2. (End)
%e A210551 From _Paul Weisenhorn_, May 14 2020: (Start)
%e A210551 First five rows of u(n,x):
%e A210551   1
%e A210551   1  2
%e A210551   1  4   3
%e A210551   1  6  10   4
%e A210551   1  8  21  20  5
%e A210551 First three polynomials u(n,x): 1, 1 + 2x, 1 + 4x + 3x^2. (End)
%t A210551 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A210551 u[n_, x_] := x*u[n - 1, x] + x*v[n - 1, x] + 1;
%t A210551 v[n_, x_] := u[n - 1, x] + (x + 1)*v[n - 1, x] + 1;
%t A210551 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A210551 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A210551 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A210551 TableForm[cu]
%t A210551 Flatten[%]    (* A172431 *)
%t A210551 Table[Expand[v[n, x]], {n, 1, z}]
%t A210551 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A210551 TableForm[cv]
%t A210551 Flatten[%]    (* A210551 *)
%Y A210551 Cf. A172431, A208510.
%K A210551 nonn,tabl
%O A210551 1,2
%A A210551 _Clark Kimberling_, Mar 22 2012