A209145 Triangle of coefficients of polynomials u(n,x) jointly generated with A122075; see the Formula section.

1, 2, 1, 4, 4, 1, 7, 10, 5, 1, 12, 22, 16, 6, 1, 20, 45, 43, 23, 7, 1, 33, 88, 104, 72, 31, 8, 1, 54, 167, 235, 199, 110, 40, 9, 1, 88, 310, 506, 506, 340, 158, 50, 10, 1, 143, 566, 1051, 1211, 956, 538, 217, 61, 11, 1, 232, 1020, 2123, 2768, 2507, 1652, 805

Offset

1,2

Comments

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

Links

Table of n, a(n) for n=1..62.

Formula

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

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

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

Example

First five rows:
1
2....1
4....4....1
7....10...5....1
12...22...16...6...1

Mathematica

First three polynomials v(n, x): 1, 2 + 3x, 4 + 4x + 4x^2.
u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := u[n - 1, x] + (x + 1)*v[n - 1, x];
v[n_, x_] := u[n - 1, x] + x*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[%]    (* A209145 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]    (* A122075 *)

Crossrefs

Cf. A209144, A208510.

Sequence in context: A220836 A008572 A209150 * A333650 A214984 A118976

Adjacent sequences: A209142 A209143 A209144 * A209146 A209147 A209148

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 06 2012

Status

approved