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

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, 126, 28, 1, 15, 91, 286, 495, 462, 210, 36, 1, 17, 120, 455, 1001, 1287, 924, 330, 45, 1, 19, 153, 680, 1820, 3003, 3003, 1716, 495, 55, 1, 21, 190, 969, 3060, 6188

Offset

1,2

Comments

Row sums: -1+odd-indexed Fibonacci numbers

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

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

Links

Table of n, a(n) for n=1..60.

Formula

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

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

where u(1,x)=1, v(1,x)=1.

Example

From Paul Weisenhorn, May 17 2020 : (Start)
First five rows of v(n.x):
  1
  3   1
  5   6   1
  7  15  10   1
  9  28  35  15  1
First three polynomials v(n,x): 1, 3 + x, 5 + 6x + x^2. (End)
From Paul Weisenhorn, May 14 2020: (Start)
First five rows of u(n,x):
  1
  1  2
  1  4   3
  1  6  10   4
  1  8  21  20  5
First three polynomials u(n,x): 1, 1 + 2x, 1 + 4x + 3x^2. (End)

Mathematica

u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := x*u[n - 1, x] + x*v[n - 1, x] + 1;
v[n_, x_] := u[n - 1, x] + (x + 1)*v[n - 1, x] + 1;
Table[Expand[u[n, x]], {n, 1, z/2}]
Table[Expand[v[n, x]], {n, 1, z/2}]
cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
TableForm[cu]
Flatten[%]    (* A172431 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]    (* A210551 *)

Crossrefs

Cf. A172431, A208510.

Sequence in context: A089028 A209758 A134083 * A113445 A108283 A208904

Adjacent sequences: A210548 A210549 A210550 * A210552 A210553 A210554

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 22 2012

Status

approved