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A210551 Triangle of coefficients of polynomials v(n,x) jointly generated with A172431; see the Formula section. 2
1, 3, 1, 5, 6, 1, 7, 15, 10, 1, 9, 28, 35, 15, 1, 11, 45, 84, 70, 21, 1, 13, 66, 165, 210, 126, 28, 1, 15, 91, 286, 495, 462, 210, 36, 1, 17, 120, 455, 1001, 1287, 924, 330, 45, 1, 19, 153, 680, 1820, 3003, 3003, 1716, 495, 55, 1, 21, 190, 969, 3060, 6188 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Row sums: -1+odd-indexed Fibonacci numbers

Alternating row sums: 1,2,0,1,2,0,1,2,0,...

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

LINKS

Table of n, a(n) for n=1..60.

FORMULA

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

v(n,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

1...2

1...3...4

1...3...9....8

1...3...10...25...16

First three polynomials v(n,x): 1, 1 + 2x , 1 + 3x + 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] + (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[%]    (* A172431 *)

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

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

TableForm[cv]

Flatten[%]    (* A210551 *)

CROSSREFS

Cf. A172431, A208510.

Sequence in context: A089028 A209758 A134083 * A113445 A108283 A208904

Adjacent sequences:  A210548 A210549 A210550 * A210552 A210553 A210554

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 22 2012

STATUS

approved

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Last modified October 21 11:37 EDT 2019. Contains 328296 sequences. (Running on oeis4.)