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!)
A136672 Riordan array ((1+x^2)/(1-x)^2, -x/(1-x)^2). 0
1, 2, -1, 4, -4, 1, 6, -11, 6, -1, 8, -24, 22, -8, 1, 10, -45, 62, -37, 10, -1, 12, -76, 147, -128, 56, -12, 1, 14, -119, 308, -366, 230, -79, 14, -1, 16, -176, 588, -912, 770, -376, 106, -16, 1, 18, -249, 1044, -2046, 2222, -1443, 574, -137, 18, -1, 20, -340, 1749, -4224, 5720, -4732, 2485, -832, 172, -20, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Row sums are: {1, 1, 1, 0, -1, -1, 0, 1, 1, 0, -1, ...}
LINKS
Pentti Haukkanen, Jorma Merikoski, Seppo Mustonen, Some polynomials associated with regular polygons, Acta Univ. Sapientiae, Mathematica, 6, 2 (2014) 178-193.
FORMULA
G.f.: g(x,t)=(2 - x)/(1 - (2 - x)*t + t^2).
EXAMPLE
{1},
{2, -1},
{4, -4, 1},
{6, -11, 6, -1},
{8, -24, 22, -8, 1},
{10, -45, 62, -37, 10, -1},
{12, -76, 147, -128, 56, -12, 1},
{14, -119,308, -366, 230, -79, 14, -1},
{16, -176, 588, -912, 770, -376, 106, -16, 1},
{18, -249, 1044, -2046, 2222, -1443, 574, -137, 18, -1},
{20, -340, 1749, -4224, 5720, -4732, 2485, -832, 172, -20, 1}
MATHEMATICA
T[n_, m_, d_] := If[ n == m, 2, If[n == d && m == d - 1, 0, If[(n == m - 1 || n == m + 1), -1, 0]]]; M[d_] := Table[T[n, m, d], {n, 1, d}, {m, 1, d}]; Table[Det[M[d]], {d, 1, 10}]; Table[Det[M[d] - x*IdentityMatrix[d]], {d, 1, 10}]; a = Join[{{1}}, Table[CoefficientList[Det[M[d] - x*IdentityMatrix[d]], x], {d, 1, 10}]]; Flatten[a] (* polynomial recursion*) Clear[p] p[x, 0] = 1; p[x, 1] = (2 - x); p[x, 2] = 4 - 4 x + x^2; p[x_, n_] := p[x, n] = (2 - x)*p[x, n - 1] - p[x, n - 2]; Table[ExpandAll[p[x, n]], {n, 0, Length[g] - 1}]
p[t_] = (2 - x)/(1 - (2 - x)*t + t^2); Table[ ExpandAll[SeriesCoefficient[ Series[p[t], {t, 0, 30}], n]], {n, 0, 10}]; a = Table[ CoefficientList[SeriesCoefficient[ Series[p[t], {t, 0, 30}], n], x], {n, 0, 10}]; Flatten[a]
{1} ~ Join ~ CoefficientList[Table[(2 - x) ChebyshevU[n - 2, 1 - x/2], {n, 2, 10}], x] // Flatten (* Eric W. Weisstein, May 10 2017 *)
CROSSREFS
Sequence in context: A208907 A200057 A136600 * A097750 A304623 A133544
KEYWORD
tabl,sign
AUTHOR
Roger L. Bagula, Apr 04 2008, Apr 12 2008
EXTENSIONS
Edited by Ralf Stephan, Feb 07 2014
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 18 22:09 EDT 2024. Contains 370951 sequences. (Running on oeis4.)