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.

0, 4, 24, 60, 480, 2580, 10200, 59100, 303600, 1396500, 7347000, 37099500, 180030000, 916552500, 4599165000, 22749787500, 114487050000, 573173362500, 2854795125000, 14307190687500, 71569168500000, 357347616562500

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

Index entries for linear recurrences with constant coefficients, signature (5, 0, 45, -225).

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