A135936 Irregular triangle read by rows: row n gives coefficients of Boubaker polynomial B_n(x) in order of decreasing exponents (another version).

1, 1, 1, 2, 1, 1, 1, 0, -2, 1, -1, -3, 1, -2, -3, 2, 1, -3, -2, 5, 1, -4, 0, 8, -2, 1, -5, 3, 10, -7, 1, -6, 7, 10, -15, 2, 1, -7, 12, 7, -25, 9, 1, -8, 18, 0, -35, 24, -2, 1, -9, 25, -12, -42, 49, -11, 1, -10, 33, -30, -42, 84, -35, 2, 1, -11, 42, -55, -30, 126, -84, 13, 1, -12, 52, -88, 0, 168, -168, 48, -2, 1, -13, 63, -130, 55, 198, -294

Offset

0,4

Comments

See A135929 and A138034 for further information.

Links

R. J. Mathar, Mar 11 2008, Table of n, a(n) for n = 0..160

Formula

Conjectures from Thomas Baruchel, Jun 03 2018: (Start)

T(n,m) = 4*A115139(n+1,m) - 3*A132460(n,m).

T(n,m) = (-1)^m * (binomial(n-m, m) - 3*binomial(n-m-1, m-1)). (End)

Example

The Boubaker polynomials B_0(x), B_1(x), B_2(x), ... are:
  1
  x
  x^2    + 2
  x^3    + x
  x^4             - 2
  x^5    - x^3  - 3*x
  x^6  - 2*x^4  - 3*x^2    + 2
  x^7  - 3*x^5  - 2*x^3  + 5*x
  x^8  - 4*x^6           + 8*x^2    - 2
  x^9  - 5*x^7  + 3*x^5 + 10*x^3  - 7*x
  ...

Maple

A135936 := proc(n, m) coeftayl( coeftayl( (1+3*t^2)/(1-x*t+t^2), t=0, n), x=0, m) ; end: for n from 0 to 25 do for m from n to 0 by -2 do printf("%d, ", A135936(n, m)) ; od; od; # R. J. Mathar, Mar 11 2008

Mathematica

T[n_, m_] := SeriesCoefficient[SeriesCoefficient[
   (1+3*t^2)/(1-x*t+t^2), {t, 0, n}], {x, 0, m}];
Table[T[n, m], {n, 0, 25}, {m, n, 0, -2}] // Flatten (* Jean-François Alcover, Mar 11 2023, after R. J. Mathar *)

Crossrefs

Cf. A138034.

Sequence in context: A331186 A375847 A372504 * A109707 A214578 A064272

Adjacent sequences: A135933 A135934 A135935 * A135937 A135938 A135939

Keyword

sign,tabf

Author

N. J. A. Sloane, Mar 09 2008

Extensions

More terms from R. J. Mathar, Mar 11 2008

Status

approved