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A210799 Triangle of coefficients of polynomials u(n,x) jointly generated with A210800; see the Formula section. 3
1, 3, 1, 5, 4, 2, 11, 13, 9, 3, 17, 32, 32, 17, 5, 35, 77, 96, 72, 32, 8, 53, 164, 254, 243, 153, 59, 13, 107, 353, 641, 739, 579, 313, 107, 21, 161, 704, 1496, 2042, 1938, 1305, 623, 192, 34, 323, 1433, 3440, 5348, 5898, 4774, 2831, 1213, 341, 55, 485 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Row n starts with A060647(n) and ends with F(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..56.

FORMULA

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

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

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

T(n,k) = T(n-1,k-1) + 3*T(n-2,k) + 2*T(n-2,k-1) + T(n-2,k-2) + a(k) with a(0) = 2, a(1) = -1, a(k) = 0 if k>1, T(1,0) = T(2,1) = 1, T(2,0) = 3 and T(n,k) = 0 if k<0 or if k>=n.

EXAMPLE

First five rows:

1

3....1

5....4....2

11...13...9....3

17...32...32...17...5

First three polynomials u(n,x): 1, 3 + x, 5 + 4x + 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 = 1; 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[%]   (* A210799 *)

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

TableForm[cv]

Flatten[%]   (* A210800 *)

CROSSREFS

Cf. A210800, A208510.

Sequence in context: A210560 A208922 A209770 * A068512 A011090 A260629

Adjacent sequences:  A210796 A210797 A210798 * A210800 A210801 A210802

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 27 2012

STATUS

approved

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Last modified October 14 03:00 EDT 2019. Contains 327995 sequences. (Running on oeis4.)