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A210550 Triangle of coefficients of polynomials v(n,x) jointly generated with A210549; see the Formula section. 3
1, 2, 2, 2, 6, 4, 2, 7, 16, 8, 2, 7, 23, 40, 16, 2, 7, 24, 71, 96, 32, 2, 7, 24, 81, 207, 224, 64, 2, 7, 24, 82, 266, 575, 512, 128, 2, 7, 24, 82, 279, 843, 1535, 1152, 256, 2, 7, 24, 82, 280, 939, 2572, 3967, 2560, 512, 2, 7, 24, 82, 280, 955, 3102, 7565, 9983 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Row sums: -1+odd-indexed Fibonacci numbers

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

LINKS

Table of n, a(n) for n=1..64.

FORMULA

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

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

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

EXAMPLE

First five rows:

2

2...2

2...6...4

2...7...16....8

2...7...28....40...16

First three polynomials v(n,x): 2, 2 + 2x , 2 + 6x + 4x^2.

MATHEMATICA

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

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

v[n_, x_] := u[n - 1, x] + 2 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[%]    (* A210549 *)

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

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

TableForm[cv]

Flatten[%]    (* A210550 *)

CROSSREFS

Cf. A210549, A208510.

Sequence in context: A158524 A054274 A053695 * A208659 A209752 A119918

Adjacent sequences:  A210547 A210548 A210549 * A210551 A210552 A210553

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 22 2012

STATUS

approved

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Last modified October 22 00:52 EDT 2019. Contains 328315 sequences. (Running on oeis4.)