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A210562 Triangle of coefficients of polynomials v(n,x) jointly generated with A210561; see the Formula section. 3
1, 2, 2, 2, 5, 4, 2, 6, 12, 8, 2, 6, 17, 28, 16, 2, 6, 18, 46, 64, 32, 2, 6, 18, 53, 120, 144, 64, 2, 6, 18, 54, 152, 304, 320, 128, 2, 6, 18, 54, 161, 424, 752, 704, 256, 2, 6, 18, 54, 162, 474, 1152, 1824, 1536, 512, 2, 6, 18, 54, 162, 485, 1372, 3056, 4352 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Last term in row n:  2^(n-1)

Limiting row:  2*3^(n-1)

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

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

u(n,x)=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,

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

First five rows:

1

2...2

2...5...4

2...6...12...8

2...6...17...28...16

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

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 + 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[%]  (* A210561 *)

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

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

TableForm[cv]

Flatten[%]  (* A210562 *)

Cf. A210561, A208510.

LINKS

Table of n, a(n) for n=1..64.

P. Bala, A note on the diagonals of a proper Riordan Array

FORMULA

From Peter Bala, Mar 06 2017: (Start)

T(n,k) = 2*T(n-1,k-1) + T(n-2,k-1).

E.g.f for the n-th subdiagonal: exp(2*x)*(2 + 2*x + 2*x^2/2! + 2*x^3/3! + ... + 2*x^(n-1)/(n-1)! + x^n/n!).

Riordan array ((1 + x)/(1 - x), x*(2 + x)).

Row sums A005409 (except for the initial term).

(End)

CROSSREFS

Row sums A005409. Cf. A208510, A210561.

Sequence in context: A194684 A076737 A246119 * A208512 A208908 A209558

Adjacent sequences:  A210559 A210560 A210561 * A210563 A210564 A210565

KEYWORD

nonn,tabl,easy

AUTHOR

Clark Kimberling, Mar 22 2012

STATUS

approved

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Last modified October 20 15:15 EDT 2019. Contains 328267 sequences. (Running on oeis4.)