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A209143 Triangle of coefficients of polynomials u(n,x) jointly generated with A209144; see the Formula section. 3
1, 2, 1, 5, 4, 11, 11, 1, 23, 28, 6, 47, 68, 23, 1, 95, 160, 74, 8, 191, 368, 216, 39, 1, 383, 832, 592, 152, 10, 767, 1856, 1552, 520, 59, 1, 1535, 4096, 3936, 1632, 270, 12, 3071, 8960, 9728, 4816, 1060, 83, 1, 6143, 19456, 23552, 13568, 3752, 436 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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

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

LINKS

Table of n, a(n) for n=1..54.

FORMULA

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

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

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

EXAMPLE

First five rows:

1

2....1

5....4

11...11...1

23...28...6

First three polynomials u(n,x):  1, 2 + x, 5 + 4x

MATHEMATICA

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

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

v[n_, x_] := u[n - 1, 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[%]    (* A209143 *)

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

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

TableForm[cv]

Flatten[%]    (* A209144 *)

CROSSREFS

Cf. A209144, A208510.

Sequence in context: A091802 A144240 A233525 * A243274 A119914 A152192

Adjacent sequences:  A209140 A209141 A209142 * A209144 A209145 A209146

KEYWORD

nonn,tabf

AUTHOR

Clark Kimberling, Mar 06 2012

STATUS

approved

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Last modified October 15 10:15 EDT 2019. Contains 328026 sequences. (Running on oeis4.)