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A210750 Triangle of coefficients of polynomials v(n,x) jointly generated with A210749; see the Formula section. 3
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified November 29 15:30 EST 2022. Contains 358431 sequences. (Running on oeis4.)