A210795 Triangle of coefficients of polynomials u(n,x) jointly generated with A210796; see the Formula section.

1, 2, 1, 3, 2, 2, 4, 5, 5, 3, 5, 8, 12, 9, 5, 6, 13, 22, 25, 17, 8, 7, 18, 38, 51, 51, 31, 13, 8, 25, 59, 98, 115, 101, 56, 21, 9, 32, 88, 166, 238, 248, 196, 100, 34, 10, 41, 124, 270, 438, 552, 520, 374, 177, 55, 11, 50, 170, 410, 762, 1090, 1234, 1064, 704

Offset

1,2

Comments

Row n starts with n and ends with F(n), where F=A000045 (Fibonacci numbers).

Column 2: A000982

Column 3: A026035

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

Links

Table of n, a(n) for n=1..64.

Formula

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

v(n,x)=(x+2)*u(n-1,x)+(x-1)*v(n-1,x),

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

Example

First five rows:
1
2...1
3...2...2
4...5...5....3
5...8...12...9...5
First three polynomials u(n,x): 1, 2 + x, 3 + 2x + 2x^2.

Mathematica

u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := u[n - 1, x] + (x + j)*v[n - 1, x] + c;
d[x_] := h + x; e[x_] := p + x;
v[n_, x_] := d[x]*u[n - 1, x] + e[x]*v[n - 1, x] + f;
j = 0; c = 1; h = 2; p = -1; f = 0;
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[%]   (* A210795 *)
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]   (* A210796 *)

Crossrefs

Cf. A210796, A208510.

Sequence in context: A208906 A120933 A209756 * A210862 A298675 A365383

Adjacent sequences: A210792 A210793 A210794 * A210796 A210797 A210798

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 26 2012

Status

approved