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A210743 Triangle of coefficients of polynomials u(n,x) jointly generated with A210744; see the Formula section. 3
1, 2, 3, 4, 8, 7, 7, 20, 25, 17, 12, 43, 76, 75, 41, 20, 88, 194, 264, 216, 99, 33, 172, 458, 770, 861, 606, 239, 54, 327, 1016, 2038, 2811, 2691, 1667, 577, 88, 608, 2161, 5012, 8206, 9689, 8149, 4517, 1393, 143, 1112, 4447, 11699, 22057, 30830 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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

2....3

4....8....7

7....20...25...17

12...43...76...75...41

First three polynomials u(n,x): 1, 2+ 3x, 4 + 8x + 7x^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. A210744, A208510.

Sequence in context: A176077 A332778 A263694 * A210750 A036712 A036706

Adjacent sequences: A210740 A210741 A210742 * A210744 A210745 A210746

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 24 2012

STATUS

approved

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Last modified December 1 01:13 EST 2022. Contains 358453 sequences. (Running on oeis4.)