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A177727 a(0)=1; a(n) = a(n-1) * Fibonacci(3+n) * Fibonacci(1+n) / (Fibonacci(n))^2, n > 1. 1
1, 3, 30, 180, 1300, 8736, 60333, 412335, 2829310, 19384200, 132882696, 910735488, 6242420665, 42785803515, 293259265950, 2010026277756, 13776931957468, 94428478367520, 647222466507045, 4436128656563175, 30405678471399166 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
Similar recurrences a(n) = a(n-1)*F(a0+n-1)*F(b0+n-1)/( F(n)*F(c0+n-1)) are:
{a0,b0,c0} = {3,2,1) in A066258.
{a0,b0,c0} = {3,1,1) in A001654.
{a0,b0,c0} = {4,1,1) in A001655 and next for 5,6 as well.
REFERENCES
Harry Hochstadt, The Functions of Mathematical Physics, Dover, New York, 1986, p. 93.
LINKS
FORMULA
G.f.: ( -1+2*x ) / ( (x-1)*(x^2+3*x+1)*(x^2-7*x+1) ). - R. J. Mathar, Nov 17 2011
a(n) = A001656(n) - 2*A001656(n-1). - R. J. Mathar, Nov 17 2011
MAPLE
with (combinat):
A177727 := proc(n)
if n = 0 then
1;
else
procname(n-1)*fibonacci(3+n)*fibonacci(1+n)/fibonacci(n)^2 ;
end if;
end proc:
seq(A177727(n), n=0..10) ; # R. J. Mathar, Nov 17 2011
MATHEMATICA
a0 = 4; b0 = 2; c0 = 1;
a[0] = 1;
a[n_] := a[n] = (Fibonacci[(a0 + n - 1)]*Fibonacci[( b0 + n - 1)]/(Fibonacci[n]*Fibonacci[(c0 + n - 1)]))*a[n - 1];
Table[a[n], {n, 0, 30}]
LinearRecurrence[{5, 15, -15, -5, 1}, {1, 3, 30, 180, 1300}, 30] (* Vincenzo Librandi, Nov 18 2011 *)
PROG
(Magma) I:=[1, 3, 30, 180, 1300]; [n le 5 select I[n] else 5*Self(n-1)+15*Self(n-2)-15*Self(n-3)-5*Self(n-4)+Self(n-5): n in [1..30]]; // Vincenzo Librandi, Nov 18 2011
CROSSREFS
Sequence in context: A013214 A013219 A013220 * A132413 A344907 A032263
KEYWORD
nonn
AUTHOR
Roger L. Bagula, May 12 2010
STATUS
approved

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Last modified May 18 07:16 EDT 2024. Contains 372618 sequences. (Running on oeis4.)