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A210879 Triangle of coefficients of polynomials v(n,x) jointly generated with A210878; see the Formula section. 3
1, 2, 2, 1, 5, 5, 1, 5, 16, 12, 1, 3, 21, 47, 29, 1, 3, 17, 79, 134, 70, 1, 3, 13, 79, 273, 373, 169, 1, 3, 13, 63, 333, 893, 1020, 408, 1, 3, 13, 55, 297, 1291, 2805, 2751, 985, 1, 3, 13, 55, 249, 1323, 4701, 8543, 7338, 2378, 1, 3, 13, 55, 233, 1147, 5525 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Leading coefficient of v(n,x):  A000129

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

Limiting row:  1,3,13,55,233,987...( Fibonacci numbers)

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

LINKS

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

FORMULA

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

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

First six rows:

1

2...2

1...5...5

1...5...16...12

1...3...21...47....29

1...3...17...79...134...70

First three polynomials v(n,x): 1, 2 + 2x, 1 + 5x + 5x^2

MATHEMATICA

u[1, x_] := 1; v[1, x_] := 1; z = 14;

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

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[%]    (* A210878 *)

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

TableForm[cv]

Flatten[%]    (* A210879 *)

CROSSREFS

Cf. A210878, A208510.

Sequence in context: A079218 A079220 A158068 * A176265 A187307 A280785

Adjacent sequences:  A210876 A210877 A210878 * A210880 A210881 A210882

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 30 2012

STATUS

approved

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Last modified November 23 19:08 EST 2017. Contains 295128 sequences.