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A210553 Triangle of coefficients of polynomials v(n,x) jointly generated with A210552; see the Formula section. 3
1, 2, 1, 3, 2, 2, 4, 3, 5, 3, 5, 4, 9, 8, 5, 6, 5, 14, 15, 15, 8, 7, 6, 20, 24, 31, 26, 13, 8, 7, 27, 35, 54, 57, 46, 21, 9, 8, 35, 48, 85, 104, 108, 80, 34, 10, 9, 44, 63, 125, 170, 209, 199, 139, 55, 11, 10, 54, 80, 175, 258, 360, 404, 366, 240, 89, 12, 11, 65, 99 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Let T(n,k) denote the term in row n, column k.

T(n,n):  A000045 (Fibonacci numbers)

T(n,n-1): A006367

T(n,n-2): A105423

T(n,1): 1,2,3,4,5,6,7,8,9,...

T(n,2): 1,2,3,4,5,6,7,8,9,...

T(n,3): A000096

T(n,4): A005563

T(n,5): A055831

T(n,6): A111694

Row sums: A000225

Alternating row sums: A052551

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

LINKS

Table of n, a(n) for n=1..70.

FORMULA

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

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

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

EXAMPLE

First five rows:

1

2...1

3...2...2

4...3...5...3

5...4...9...8...5

First three polynomials v(n,x): 1, 2 + x , 3 + 2x + 2x^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_] := x*u[n - 1, 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[%]   (* A210552 *)

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

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

TableForm[cv]

Flatten[%]   (* A210553 *)

Table[u[n, x] /. x -> 1, {n, 1, z}]  (* A000225 *)

Table[v[n, x] /. x -> 1, {n, 1, z}]  (* A000225 *)

Table[u[n, x] /. x -> -1, {n, 1, z}] (* A094024 *)

Table[v[n, x] /. x -> -1, {n, 1, z}] (* A052551 *)

CROSSREFS

Cf. A210552, A208510.

Sequence in context: A144329 A141157 A137948 * A269456 A208906 A120933

Adjacent sequences:  A210550 A210551 A210552 * A210554 A210555 A210556

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 22 2012

STATUS

approved

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Last modified October 20 13:48 EDT 2019. Contains 328258 sequences. (Running on oeis4.)