The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
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!)
A091054 Expansion of (1 - 5*x - 2*x^2) / ((1 - x)*(1 + 2*x)*(1 - 6*x)). 3
1, 0, 6, 18, 138, 762, 4698, 27930, 168090, 1007514, 6047130, 36278682, 217680282, 1306065306, 7836424602, 47018482074, 282111023514, 1692665878938, 10155995797914, 60935973738906, 365615844530586, 2193695062989210 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
Closed walks of length n at a vertex of the Johnson graph J(5,2).
6^n = a(n) + 6*A091055(n) + 3*4*A091056(n).
LINKS
Eric Weisstein's World of Mathematics, Johnson Graph
FORMULA
a(n) = (6^n + 5*(-2)^n + 4)/10.
a(n) = 5*a(n-1) + 8*a(n-2) - 12*a(n-3) for n>2. - Colin Barker, Dec 26 2019
E.g.f.: (exp(6*x) + 5*exp(-2*x) + 4*exp(x))/10. - G. C. Greubel, Dec 27 2019
MAPLE
seq( (6^n +5*(-2)^n +4)/10, n=0..30); # G. C. Greubel, Dec 27 2019
MATHEMATICA
Table[(6^n +5*(-2)^n +4)/10, {n, 0, 30}] (* G. C. Greubel, Dec 27 2019 *)
LinearRecurrence[{5, 8, -12}, {1, 0, 6}, 30] (* Harvey P. Dale, Oct 21 2021 *)
PROG
(PARI) Vec((1 - 5*x - 2*x^2) / ((1 - x)*(1 + 2*x)*(1 - 6*x)) + O(x^25)) \\ Colin Barker, Dec 26 2019
(PARI) vector(31, n, (6^(n-1) +5*(-2)^(n-1) +4)/10) \\ G. C. Greubel, Dec 27 2019
(Magma) [(6^n +5*(-2)^n +4)/10: n in [0..30]]; // G. C. Greubel, Dec 27 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 25); Coefficients(R!( (1 - 5*x - 2*x^2) / ((1 - x)*(1 + 2*x)*(1 - 6*x)))); // Marius A. Burtea, Dec 29 2019
(Sage) [(6^n +5*(-2)^n +4)/10 for n in (0..30)] # G. C. Greubel, Dec 27 2019
(GAP) List([0..30], n-> (6^n +5*(-2)^n +4)/10); # G. C. Greubel, Dec 27 2019
CROSSREFS
Sequence in context: A003496 A009582 A222913 * A012774 A306656 A027744
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Dec 17 2003
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 May 30 16:58 EDT 2024. Contains 372971 sequences. (Running on oeis4.)