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

 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 Colin Barker, Table of n, a(n) for n = 0..1000 Eric Weisstein's World of Mathematics, Johnson Graph Index entries for linear recurrences with constant coefficients, signature (5,8,-12). 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:=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 Cf. A091055, A091056. Sequence in context: A003496 A009582 A222913 * A012774 A306656 A027744 Adjacent sequences: A091051 A091052 A091053 * A091055 A091056 A091057 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.

Last modified May 30 16:58 EDT 2024. Contains 372971 sequences. (Running on oeis4.)