A208512 Triangle of coefficients of polynomials v(n,x) jointly generated with A208511; see the Formula section.

1, 2, 2, 2, 5, 4, 2, 7, 12, 8, 2, 9, 21, 28, 16, 2, 11, 32, 58, 64, 32, 2, 13, 45, 101, 152, 144, 64, 2, 15, 60, 159, 296, 384, 320, 128, 2, 17, 77, 234, 513, 824, 944, 704, 256, 2, 19, 96, 328, 822, 1554, 2208, 2272, 1536, 512, 2, 21, 117, 443, 1244, 2685

Offset

1,2

Comments

Alternating row sums are signed Fibonacci numbers (A000045).

Links

Table of n, a(n) for n=1..61.

Formula

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

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

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

Example

First five rows:
1
2...2
2...5...4
2...7...12...8
2...9...21...28...16
First five polynomials v(n,x):
1
2 + 2x
2 + 5x + 4x^2
2 + 7x + 12x^2 + 8x^3
2 + 9x + 21x^2 + 28x^3 + 16x^4

Mathematica

u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := u[n - 1, x] + x*v[n - 1, x];
v[n_, x_] := u[n - 1, x] + 2 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[%]  (* A208511 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]    (* A208512 *)

Crossrefs

Cf. A208511.

Sequence in context: A076737 A246119 A210562 * A208908 A209558 A209772

Adjacent sequences: A208509 A208510 A208511 * A208513 A208514 A208515

Keyword

nonn,tabl

Author

Clark Kimberling, Feb 28 2012

Status

approved