A182754 a(1) = 1, a(2) = 21, a(n) = 77*a(n-2) for n>=3.

1, 21, 77, 1617, 5929, 124509, 456533, 9587193, 35153041, 738213861, 2706784157, 56842467297, 208422380089, 4376869981869, 16048523266853, 337018988603913, 1235736291547681, 25950462122501301, 95151694449171437, 1998185583432600177, 7326680472586200649

Offset: 1

Author

Jaroslav Krizek, Nov 27 2010

Keywords

• nonn
• easy

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).

Examples

			For n = 4; a(2) = 21, a(3) = 77, a(4) = 1617 before [(21+77)*(21+1617)*(77+1617)]  / (21*77*1617) = 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).

Crossrefs

Cf. A182751 - A182757, A038754.

Programs

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

Mathematica

LinearRecurrence[{0,77},{1,21},30] (* Harvey P. Dale, Sep 05 2013 *)

PARI

A182754(n)=if(n%2,77^(n\2),77^(n\2-1)*21)

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

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)

Extensions

More terms from Harvey P. Dale, Sep 05 2013