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A209145 Triangle of coefficients of polynomials u(n,x) jointly generated with A122075; see the Formula section. 2
1, 2, 1, 4, 4, 1, 7, 10, 5, 1, 12, 22, 16, 6, 1, 20, 45, 43, 23, 7, 1, 33, 88, 104, 72, 31, 8, 1, 54, 167, 235, 199, 110, 40, 9, 1, 88, 310, 506, 506, 340, 158, 50, 10, 1, 143, 566, 1051, 1211, 956, 538, 217, 61, 11, 1, 232, 1020, 2123, 2768, 2507, 1652, 805 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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

LINKS

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

FORMULA

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

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

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

EXAMPLE

First five rows:

1

2....1

4....4....1

7....10...5....1

12...22...16...6...1

MATHEMATICA

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

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

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

v[n_, x_] := 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[%]    (* A209145 *)

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

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

TableForm[cv]

Flatten[%]    (* A122075 *)

CROSSREFS

Cf. A209144, A208510.

Sequence in context: A220836 A008572 A209150 * A214984 A118976 A210235

Adjacent sequences:  A209142 A209143 A209144 * A209146 A209147 A209148

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 06 2012

STATUS

approved

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Last modified October 22 00:52 EDT 2019. Contains 328315 sequences. (Running on oeis4.)