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A209776 Triangle of coefficients of polynomials v(n,x) jointly generated with A209773; see the Formula section. 3
1, 3, 2, 5, 8, 4, 9, 22, 22, 8, 15, 52, 78, 56, 16, 25, 112, 226, 242, 136, 32, 41, 228, 580, 828, 692, 320, 64, 67, 446, 1374, 2456, 2726, 1872, 736, 128, 109, 848, 3074, 6612, 9158, 8336, 4864, 1664, 256, 177, 1578, 6590, 16590, 27564, 31250 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Alternating row sums: 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..51.

FORMULA

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

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

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

EXAMPLE

First five rows:

1

3....2

5....8....4

9....22...22...8

15...52...78...56...16

First three polynomials v(n,x): 1, 3 + 2x , 5 + 8x + 4x^2.

MATHEMATICA

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

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

v[n_, x_] := (x + 1)*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[%]    (* A209775 *)

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

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

TableForm[cv]

Flatten[%]    (* A209776 *)

CROSSREFS

Cf. A209675, A208510.

Sequence in context: A209757 A208932 A189951 * A019594 A085167 A127299

Adjacent sequences:  A209773 A209774 A209775 * A209777 A209778 A209779

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 15 2012

STATUS

approved

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Last modified October 19 11:09 EDT 2019. Contains 328216 sequences. (Running on oeis4.)