A209749 Triangle of coefficients of polynomials u(n,x) jointly generated with A209750; see the Formula section.

1, 1, 2, 2, 4, 3, 2, 8, 9, 4, 3, 11, 21, 17, 5, 3, 17, 37, 47, 29, 6, 4, 21, 63, 101, 95, 46, 7, 4, 29, 93, 193, 241, 178, 69, 8, 5, 34, 138, 329, 519, 522, 314, 99, 9, 5, 44, 186, 533, 999, 1264, 1050, 527, 137, 10, 6, 50, 255, 805, 1776, 2710, 2845, 1991, 848

Offset

1,3

Comments

Alternating row sums: 1,-1,1,-1,1,-1,1,-1,...

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

Links

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

Formula

u(n,x)=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
1...2
2...4....3
2...8....9....4
3...11...21...17...5
First three polynomials u(n,x): 1, 1 + 2x, 2 + 4x + 3x^2.

Mathematica

u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := 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[%]    (* A209749 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]    (* A209750 *)

Crossrefs

Cf. A209750, A208510.

Sequence in context: A355476 A328932 A341148 * A248345 A094953 A332862

Adjacent sequences: A209746 A209747 A209748 * A209750 A209751 A209752

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 14 2012

Status

approved