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A210795 Triangle of coefficients of polynomials u(n,x) jointly generated with A210796; see the Formula section. 3
1, 2, 1, 3, 2, 2, 4, 5, 5, 3, 5, 8, 12, 9, 5, 6, 13, 22, 25, 17, 8, 7, 18, 38, 51, 51, 31, 13, 8, 25, 59, 98, 115, 101, 56, 21, 9, 32, 88, 166, 238, 248, 196, 100, 34, 10, 41, 124, 270, 438, 552, 520, 374, 177, 55, 11, 50, 170, 410, 762, 1090, 1234, 1064, 704 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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

Column 2: A000982

Column 3: A026035

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

LINKS

Table of n, a(n) for n=1..64.

FORMULA

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

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

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

EXAMPLE

First five rows:

1

2...1

3...2...2

4...5...5....3

5...8...12...9...5

First three polynomials u(n,x): 1, 2 + x, 3 + 2x + 2x^2.

MATHEMATICA

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

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

d[x_] := h + x; e[x_] := p + x;

v[n_, x_] := d[x]*u[n - 1, x] + e[x]*v[n - 1, x] + f;

j = 0; c = 1; h = 2; p = -1; f = 0;

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[%]   (* A210795 *)

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

TableForm[cv]

Flatten[%]   (* A210796 *)

CROSSREFS

Cf. A210796, A208510.

Sequence in context: A208906 A120933 A209756 * A210862 A298675 A144154

Adjacent sequences:  A210792 A210793 A210794 * A210796 A210797 A210798

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 26 2012

STATUS

approved

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Last modified October 20 10:45 EDT 2019. Contains 328257 sequences. (Running on oeis4.)