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 A112611 a(n) = 5*a(n-1) + 45*a(n-3) - 225*a(n-4), a(0)=0, a(1)=4, a(2)=24, a(3)=60, a(4)=480. 1
 0, 4, 24, 60, 480, 2580, 10200, 59100, 303600, 1396500, 7347000, 37099500, 180030000, 916552500, 4599165000, 22749787500, 114487050000, 573173362500, 2854795125000, 14307190687500, 71569168500000, 357347616562500 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Scale and initial conditions changed compared to the reference to get integer output. REFERENCES Taylor Booth, Sequential Machines and Automata Theory, John Wiley and Sons, New York, 1967, Pages 454-455. LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 FORMULA G.f.: 4*x*(1+x-15*x^2)/((1-5*x)*(1-45*x^3)). [Sep 28 2009] a(n) = (1/4)*(3*5^n - 3*b(n) + b(n-1) + 21*b(n-2)), where b(n) = (45)^(n/3)*A079978(n). - G. C. Greubel, Jul 30 2022 MATHEMATICA M = {{1, 4, 0, 0}, {0, 0, 4, 1}, {4, 1, 0, 0}, {0, 0, 1, 4}}; w[0]= {0, 1, 1, 1}; w[n_]:= w[n]= M.w[n-1]; a[n_]:= a[n]= w[n][[1]]; Table[a[n], {n, 0, 50}] LinearRecurrence[{5, 0, 45, -225}, {0, 4, 24, 60}, 60] (* G. C. Greubel, Jul 30 2022 *) PROG (Magma) I:=[0, 4, 24, 60]; [n le 4 select I[n] else 5*Self(n-1) +45*Self(n-3) -225*Self(n-4): n in [1..41]]; // G. C. Greubel, Jul 30 2022 (SageMath) def b(n): return (45)^(n/3)*( (2^((n%3))%2) ) def a(n): return (1/4)*(3*5^n -3*b(n) +b(n-1) +21*b(n-2)) [a(n) for n in (0..50)] # G. C. Greubel, Jul 30 2022 CROSSREFS Cf. A079978, A104180, A104181. Sequence in context: A085250 A166870 A124350 * A363092 A212066 A336039 Adjacent sequences: A112608 A112609 A112610 * A112612 A112613 A112614 KEYWORD nonn,easy AUTHOR Roger L. Bagula, Feb 27 2006 EXTENSIONS Definition replaced by recurrence by the Associate Editors of the OEIS, Sep 28 2009 STATUS approved

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Last modified February 28 08:11 EST 2024. Contains 370393 sequences. (Running on oeis4.)