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A208512 Triangle of coefficients of polynomials v(n,x) jointly generated with A208511; see the Formula section. 3
1, 2, 2, 2, 5, 4, 2, 7, 12, 8, 2, 9, 21, 28, 16, 2, 11, 32, 58, 64, 32, 2, 13, 45, 101, 152, 144, 64, 2, 15, 60, 159, 296, 384, 320, 128, 2, 17, 77, 234, 513, 824, 944, 704, 256, 2, 19, 96, 328, 822, 1554, 2208, 2272, 1536, 512, 2, 21, 117, 443, 1244, 2685 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Alternating row sums are signed Fibonacci numbers (A000045).

LINKS

Table of n, a(n) for n=1..61.

FORMULA

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

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:

1

2...2

2...5...4

2...7...12...8

2...9...21...28...16

First five polynomials v(n,x):

1

2 + 2x

2 + 5x + 4x^2

2 + 7x + 12x^2 + 8x^3

2 + 9x + 21x^2 + 28x^3 + 16x^4

MATHEMATICA

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

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

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[%]  (* A208511 *)

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

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

TableForm[cv]

Flatten[%]    (* A208512 *)

CROSSREFS

Cf. A208511.

Sequence in context: A076737 A246119 A210562 * A208908 A209558 A209772

Adjacent sequences:  A208509 A208510 A208511 * A208513 A208514 A208515

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Feb 28 2012

STATUS

approved

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Last modified October 15 05:43 EDT 2019. Contains 328026 sequences. (Running on oeis4.)