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A210219 Triangle of coefficients of polynomials u(n,x) jointly generated with A210220; see the Formula section. 3
1, 2, 1, 3, 4, 1, 4, 9, 7, 1, 5, 16, 22, 11, 1, 6, 25, 50, 46, 16, 1, 7, 36, 95, 130, 86, 22, 1, 8, 49, 161, 295, 296, 148, 29, 1, 9, 64, 252, 581, 791, 610, 239, 37, 1, 10, 81, 372, 1036, 1792, 1897, 1163, 367, 46, 1, 11, 100, 525, 1716, 3612, 4900, 4166 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

First two terms in row n: n,(n-1)^2; last term: 1

Period of alternating row sums: (1,1,0)

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

Apparently this is A071920 without the marginal zeros, read downwards antidiagonals, or T(n,k) = A071922(n,k). - R. J. Mathar, May 17 2014

LINKS

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

FORMULA

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

v(n,x)=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

2...1

3...4....1

4...9....7....1

5...16...22...11...1

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

MATHEMATICA

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

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

v[n_, x_] := 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[%] (* A210219 *)

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

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

TableForm[cv]

Flatten[%] (* A210220 *)

CROSSREFS

Cf. A210220, A208510, A001906 (row sums).

Sequence in context: A103283 A104698 A067066 * A125103 A171275 A335312

Adjacent sequences: A210216 A210217 A210218 * A210220 A210221 A210222

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 19 2012

STATUS

approved

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Last modified December 2 17:17 EST 2022. Contains 358510 sequences. (Running on oeis4.)