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A210739 Triangle of coefficients of polynomials u(n,x) jointly generated with A210740; see the Formula section. 3
1, 1, 3, 1, 4, 8, 1, 4, 14, 21, 1, 4, 15, 46, 55, 1, 4, 15, 55, 145, 144, 1, 4, 15, 56, 196, 444, 377, 1, 4, 15, 56, 208, 678, 1331, 987, 1, 4, 15, 56, 209, 764, 2282, 3926, 2584, 1, 4, 15, 56, 209, 779, 2762, 7499, 11434, 6765, 1, 4, 15, 56, 209, 780, 2892 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Rows end with even-indexed Fibonacci numbers

Limiting row: A001353

Row sums:  A003562

Alternating row sums:  A000975 (signed)

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

LINKS

Table of n, a(n) for n=1..62.

FORMULA

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

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

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

EXAMPLE

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

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

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

First five rows:

1

1...3

1...4...8

1...4...14...21

1...4...15...46...55

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

MATHEMATICA

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

u[n_, x_] := 2 x*u[n - 1, x] + x*v[n - 1, x] + 1;

v[n_, x_] := (x + 1)*u[n - 1, x] + 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[%]    (* A210739 *)

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

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

TableForm[cv]

Flatten[%]    (* A210740 *)

CROSSREFS

Cf. A210740, A208510.

Sequence in context: A217151 A081255 A005371 * A193605 A193667 A205878

Adjacent sequences:  A210736 A210737 A210738 * A210740 A210741 A210742

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 24 2012

STATUS

approved

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Last modified October 23 14:54 EDT 2019. Contains 328345 sequences. (Running on oeis4.)