OFFSET
1,2
COMMENTS
For n >= 3, a(n) = the smallest number h > a(n-1) such that [[a(n-2) + a(n-1)] * [a(n-2) + a(n)] * [a(n-1) + a(n)]] / [a(n-2) * a(n-1) * a(n)] is an integer (= 104).
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (0,77).
FORMULA
a(2*n) = 21*a(2*n-1), a(2*n+1) = (11/3)*a(2*n).
G.f.: x*(1+21*x) / ( 1 - 77*x^2 ).
From Colin Barker, Jan 11 2018: (Start)
a(n) = 3*7^(n/2)*11^(n/2-1) for n even.
a(n) = 77^((n-1)/2) for n odd. (End)
EXAMPLE
For n = 4; a(2) = 21, a(3) = 77, a(4) = 1617 before [(21+77)*(21+1617)*(77+1617)] / (21*77*1617) = 104.
MATHEMATICA
LinearRecurrence[{0, 77}, {1, 21}, 30] (* Harvey P. Dale, Sep 05 2013 *)
PROG
(PARI) A182754(n)=if(n%2, 77^(n\2), 77^(n\2-1)*21)
(Magma) I:=[1, 21]; [n le 2 select I[n] else 77*Self(n-2): n in [1..30]]; // G. C. Greubel, Jan 11 2018
(PARI) Vec(x*(1 + 21*x) / (1 - 77*x^2) + O(x^40)) \\ Colin Barker, Jan 11 2018
(Python)
def aupton(nn):
dmo = [1, 21, 77]
for n in range(3, nn+1): dmo.append(77*dmo[-2])
return dmo[:nn]
print(aupton(21)) # Michael S. Branicky, Jan 21 2021
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Jaroslav Krizek, Nov 27 2010
EXTENSIONS
More terms from Harvey P. Dale, Sep 05 2013
STATUS
approved