|
Search: id:A135929
|
|
|
| A135929 |
|
Triangle read by rows: row n gives coefficients of Boubaker polynomial B_n(x) in order of decreasing exponents. |
|
+0
17
|
|
| 1, 1, 0, 1, 0, 2, 1, 0, 1, 0, 1, 0, 0, 0, -2, 1, 0, -1, 0, -3, 0, 1, 0, -2, 0, -3, 0, 2, 1, 0, -3, 0, -2, 0, 5, 0, 1, 0, -4, 0, 0, 0, 8, 0, -2, 1, 0, -5, 0, 3, 0, 10, 0, -7, 0, 1, 0, -6, 0, 7, 0, 10, 0, -15, 0, 2, 1, 0, -7, 0, 12, 0, 7, 0, -25, 0, 9, 0, 1, 0, -8, 0, 18, 0, 0, 0, -35, 0, 24, 0, -2, 1
(list; table; graph; listen)
|
|
|
OFFSET
|
0,6
|
|
|
COMMENT
|
See A138034 for references.
|
|
REFERENCES
|
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972; see Chapter 22.
|
|
FORMULA
|
Boubaker polynomials have generating function (1+3*t^2)/(1-x*t+t^2). They are related to the Chebyshev polynomials S_n(x), which have g.f. 1/(1-x*t+t^2) (see Abramowitz and Stegun).
|
|
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
|
A135929 := proc(n, m) coeftayl( coeftayl( (1+3*t^2)/(1-x*t+t^2), t=0, n), x=0, n-m) ; end proc: seq(seq(A135929(n, m), m=0..n), n=0..14) ; [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 03 2009]
|
|
CROSSREFS
|
Cf. A138034, A135936.
Sequence in context: A157424 A144961 A144627 this_sequence A080733 A080732 A088568
Adjacent sequences: A135926 A135927 A135928 this_sequence A135930 A135931 A135932
|
|
KEYWORD
|
sign,tabl,new
|
|
AUTHOR
|
N. J. A. Sloane (njas(AT)research.att.com), Mar 09 2008
|
|
EXTENSIONS
|
Extended by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 03 2009
|
|
|
Search completed in 0.002 seconds
|
