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A210232 Triangle of coefficients of polynomials v(n,x) jointly generated with A210231; see the Formula section. 3
1, 2, 2, 3, 5, 3, 4, 10, 10, 4, 5, 16, 25, 18, 5, 6, 24, 48, 54, 30, 6, 7, 33, 84, 123, 106, 47, 7, 8, 44, 132, 246, 282, 194, 70, 8, 9, 56, 198, 438, 637, 594, 336, 100, 9, 10, 70, 280, 730, 1272, 1504, 1170, 556, 138, 10, 11, 85, 385, 1140, 2337, 3337, 3301 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

First and last terms of row n are n.

Alternating row sums: 1,0,1,0,1,0,1,0,1,0,...

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

LINKS

Table of n, a(n) for n=1..62.

FORMULA

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

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

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

EXAMPLE

First five rows:

1

2...2

3...5....3

4...10...10...4

5...16...25...16...5

First three polynomials v(n,x): 1, 2 + 2x , 3 + 5x + 3x^2.

MATHEMATICA

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

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

v[n_, x_] := (x + 1)*u[n - 1, x] + 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[%]     (* A210231 *)

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

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

TableForm[cv]

Flatten[%]     (* A210232 *)

CROSSREFS

Cf. A210231, A208510.

Sequence in context: A210565 A125101 A208519 * A047666 A285935 A209568

Adjacent sequences:  A210229 A210230 A210231 * A210233 A210234 A210235

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 20 2012

STATUS

approved

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Last modified October 18 05:07 EDT 2019. Contains 328145 sequences. (Running on oeis4.)