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A210744 Triangle of coefficients of polynomials v(n,x) jointly generated with A210743; see the Formula section. 3
1, 3, 1, 6, 6, 3, 11, 18, 18, 7, 19, 45, 63, 49, 17, 32, 100, 182, 200, 133, 41, 53, 208, 464, 658, 613, 356, 99, 87, 413, 1094, 1886, 2244, 1823, 944, 239, 142, 794, 2437, 4940, 7093, 7325, 5302, 2483, 577, 231, 1490, 5206, 12113, 20311, 25220 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Row n starts with -2+F(n+3), where F=A000045 (Fibonacci numbers) and ends with A001333(n-1).

Alternating row sums: 1,2,3,4,5,6,7,8,...

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

LINKS

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

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

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

EXAMPLE

First five rows:

1

3....1

6....6....3

11...18...18...7

19...45...63...49...17

First three polynomials v(n,x): 1, 3 + x, 6 + 6x +3x^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] + 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[%] (* A210743 *)

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

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

TableForm[cv]

Flatten[%] (* A210744 *)

CROSSREFS

Cf. A210743, A208510.

Sequence in context: A116412 A089511 A246257 * A242729 A112692 A291217

Adjacent sequences: A210741 A210742 A210743 * A210745 A210746 A210747

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 24 2012

STATUS

approved

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Last modified November 27 07:58 EST 2022. Contains 358362 sequences. (Running on oeis4.)