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A210037 Triangle of coefficients of polynomials u(n,x) jointly generated with A210038; see the Formula section. 3
1, 3, 7, 1, 15, 5, 1, 31, 17, 6, 1, 63, 49, 24, 7, 1, 127, 129, 80, 32, 8, 1, 255, 321, 240, 120, 41, 9, 1, 511, 769, 672, 400, 170, 51, 10, 1, 1023, 1793, 1792, 1232, 620, 231, 62, 11, 1, 2047, 4097, 4608, 3584, 2072, 912, 304, 74, 12, 1, 4095, 9217 (list; 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..58.

FORMULA

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

v(n,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

3

7....1

15...5....1

31...17...6...1

First three polynomials u(n,x): 1, 3, 7 + x.

MATHEMATICA

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

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

v[n_, 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[%]    (* A210037 *)

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

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

TableForm[cv]

Flatten[%]    (* A210038 *)

CROSSREFS

Cf. A210038, A208510.

Sequence in context: A124138 A135561 A196231 * A210197 A324715 A316665

Adjacent sequences:  A210034 A210035 A210036 * A210038 A210039 A210040

KEYWORD

nonn,tabf

AUTHOR

Clark Kimberling, Mar 17 2012

STATUS

approved

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Last modified October 14 09:57 EDT 2019. Contains 327995 sequences. (Running on oeis4.)