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A210188 Triangle of coefficients of polynomials v(n,x) jointly generated with A210187; see the Formula section. 3
1, 2, 2, 3, 7, 2, 4, 16, 11, 2, 5, 30, 36, 15, 2, 6, 50, 91, 64, 19, 2, 7, 77, 196, 204, 100, 23, 2, 8, 112, 378, 540, 385, 144, 27, 2, 9, 156, 672, 1254, 1210, 650, 196, 31, 2, 10, 210, 1122, 2640, 3289, 2366, 1015, 256, 35, 2, 11, 275, 1782, 5148, 8008 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Row sums:  -1+(odd-indexed Fibonacci numbers): 1,4,12,...

Period of alternating row sums: (1,-,-2,-3,-2,0)

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

LINKS

Table of n, a(n) for n=1..60.

FORMULA

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

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

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

EXAMPLE

First five rows:

1

2...2

3...7....2

4...16...11...2

5...30...36...15...2

First three polynomials v(n,x): 1, 2 + 2x , 3 + 7x + 2x^2.

MATHEMATICA

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

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

v[n_, x_] := x*u[n - 1, x] + (x + 1)*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[%]    (* A210187 *)

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

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

TableForm[cv]

Flatten[%]    (* A210188 *)

CROSSREFS

Cf. A210187, A208510.

Sequence in context: A260161 A195694 A021451 * A183442 A296019 A134232

Adjacent sequences:  A210185 A210186 A210187 * A210189 A210190 A210191

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 18 2012

STATUS

approved

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Last modified October 21 11:42 EDT 2019. Contains 328296 sequences. (Running on oeis4.)