A210750 Triangle of coefficients of polynomials v(n,x) jointly generated with A210749; see the Formula section.

1, 2, 3, 4, 8, 7, 7, 21, 24, 15, 12, 46, 78, 64, 31, 20, 96, 205, 247, 160, 63, 33, 190, 501, 756, 712, 384, 127, 54, 365, 1140, 2109, 2483, 1929, 896, 255, 88, 684, 2480, 5404, 7764, 7538, 5002, 2048, 511, 143, 1259, 5199, 13083, 22070, 26058

Offset

1,2

Comments

Row n starts with -1+F(n+2) and ends with -1+2^n, where F=A000045 (Fibonacci numbers).

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

Links

Table of n, a(n) for n=1..51.

Formula

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

v(n,x)=(x+1)*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....3
4....8....7
7....21...24...15
12...46...78...64...31
First three polynomials v(n,x): 1, 2 + 3x, 4 + 8x +7x^2

Mathematica

u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := (x + 1)*u[n - 1, x] + v[n - 1, x] + 1;
v[n_, x_] := (x + 1)*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[%]    (* A210749 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]    (* A210750 *)

Crossrefs

Cf. A210749, A208510.

Sequence in context: A332778 A263694 A210743 * A036712 A036706 A336785

Adjacent sequences: A210747 A210748 A210749 * A210751 A210752 A210753

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 25 2012

Status

approved