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A210748 Triangle of coefficients of polynomials v(n,x) jointly generated with A210747; see the Formula section. 3
1, 3, 2, 6, 10, 5, 11, 29, 32, 13, 19, 71, 118, 99, 34, 32, 156, 352, 437, 299, 89, 53, 322, 919, 1521, 1526, 887, 233, 87, 636, 2205, 4559, 6036, 5117, 2595, 610, 142, 1218, 4979, 12373, 20320, 22591, 16653, 7508, 1597, 231, 2279, 10751, 31233 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Row n starts with -2+F(n+3) and ends with F(2n-1), where F=A000045 (Fibonacci numbers).

Row sums: A002450

Alternating row sums: 1,1,1,1,1,1,1,1,1,...(A000012)

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

LINKS

Table of n, a(n) for n=1..49.

FORMULA

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

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

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

EXAMPLE

First five rows:

1

3....2

6....10...5

11...29...32....13

19...71...118...99...34

First three polynomials v(n,x): 1, 3 + 2x, 6 + 10x +5x^2

MATHEMATICA

u[1, x_] := 1; v[1, x_] := 1; z = 16;

u[n_, x_] := 2 x*u[n - 1, x] + (x + 1)*v[n - 1, x] + 1;

v[n_, x_] := (x + 1)*u[n - 1, x] + (x + 1)*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[%] (* A210747 *)

Table[Expand[v[n, x]], {n, 1, z}]

cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];

TableForm[cv]

Flatten[%] (* A210748 *)

Table[u[n, x] /. x -> 1, {n, 1, z}] (* A002450 *)

Table[v[n, x] /. x -> 1, {n, 1, z}] (* A002450 *)

Table[u[n, x] /. x -> -1, {n, 1, z}] (* A077925 *)

Table[v[n, x] /. x -> -1, {n, 1, z}] (* A000012 *)

CROSSREFS

Cf. A210747, A208510.

Sequence in context: A245609 A072765 A210756 * A331889 A340612 A109876

Adjacent sequences: A210745 A210746 A210747 * A210749 A210750 A210751

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 25 2012

STATUS

approved

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Last modified December 1 03:09 EST 2022. Contains 358454 sequences. (Running on oeis4.)