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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
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
Sequence in context: A085250 A166870 A124350 * A363092 A212066 A336039
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.)