login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A135936 Irregular triangle read by rows: row n gives coefficients of Boubaker polynomial B_n(x) in order of decreasing exponents (another version). 4
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 (list; graph; refs; listen; history; text; internal format)
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: A277045 A146061 A331186 * A109707 A214578 A064272
KEYWORD
sign,tabf
AUTHOR
N. J. A. Sloane, Mar 09 2008
EXTENSIONS
More terms from R. J. Mathar, Mar 11 2008
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 19 03:17 EDT 2024. Contains 370952 sequences. (Running on oeis4.)