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A210187 Triangle of coefficients of polynomials u(n,x) jointly generated with A210188; see the Formula section. 3
1, 3, 6, 2, 10, 9, 2, 15, 25, 13, 2, 21, 55, 49, 17, 2, 28, 105, 140, 81, 21, 2, 36, 182, 336, 285, 121, 25, 2, 45, 294, 714, 825, 506, 169, 29, 2, 55, 450, 1386, 2079, 1716, 819, 225, 33, 2, 66, 660, 2508, 4719, 5005, 3185, 1240, 289, 37, 2, 78, 935, 4290 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Row sums: even-indexed Fibonacci numbers: 1,3,8,21,55,...

Column 1:  triangular numbers: A000217

Alternating row sums:  periodic with period (1,3,4,3,1,0)

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

LINKS

Table of n, a(n) for n=1..59.

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

3

6....2

10...9....2

15...25...13...2

First three polynomials u(n,x): 1, 3, 6 + 2x.

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. A210188, A208510.

Sequence in context: A309609 A266971 A257106 * A210189 A257506 A210035

Adjacent sequences:  A210184 A210185 A210186 * A210188 A210189 A210190

KEYWORD

nonn,tabf

AUTHOR

Clark Kimberling, Mar 18 2012

STATUS

approved

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Last modified October 20 22:44 EDT 2019. Contains 328291 sequences. (Running on oeis4.)