A210191 Triangle of coefficients of polynomials u(n,x) jointly generated with A210192; see the Formula section.

1, 3, 5, 3, 7, 10, 3, 9, 21, 16, 3, 11, 36, 47, 22, 3, 13, 55, 104, 85, 28, 3, 15, 78, 195, 236, 135, 34, 3, 17, 105, 328, 535, 456, 197, 40, 3, 19, 136, 511, 1058, 1227, 788, 271, 46, 3, 21, 171, 752, 1897, 2820, 2471, 1256, 357, 52, 3, 23, 210, 1059, 3160

Offset

1,2

Comments

Period of alternating row sums: (1,3,2,0)

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

Links

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

Formula

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

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

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

Example

First five rows:
1
3
5...3
7...10...3
9...21...16...3
First three polynomials u(n,x): 1, 3, 5 + 3x.

Mathematica

u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := u[n - 1, x] + v[n - 1, x] + 1;
v[n_, x_] := 2 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[%]    (* A210191 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]    (* A210192 *)

Crossrefs

Cf. A210192, A208510.

Sequence in context: A345280 A240499 A248511 * A110465 A354528 A328915

Adjacent sequences: A210188 A210189 A210190 * A210192 A210193 A210194

Keyword

nonn,tabf

Author

Clark Kimberling, Mar 18 2012

Status

approved