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A199115
a(n) = 5*4^n+1.
3
6, 21, 81, 321, 1281, 5121, 20481, 81921, 327681, 1310721, 5242881, 20971521, 83886081, 335544321, 1342177281, 5368709121, 21474836481, 85899345921, 343597383681, 1374389534721, 5497558138881, 21990232555521, 87960930222081
OFFSET
0,1
COMMENTS
An Engel expansion of 4/5 to the base 4 as defined in A181565, with the associated series expansion 4/5 = 4/6 + 4^2/(6*21) + 4^3/(6*21*81) + 4^4/(6*21*81*321) + ... . Cf. A136412 and A140660. - Peter Bala, Oct 29 2013
FORMULA
a(n) = 3*A136412(n).
a(n) = 4*a(n-1)-3.
a(n) = 5*a(n-1)-4*a(n-2).
G.f.: 3*(2-3*x)/((1-x)*(1-4*x)). - Bruno Berselli, Nov 04 2011
MATHEMATICA
5*4^Range[0, 30]+1 (* or *) LinearRecurrence[{5, -4}, {6, 21}, 30] (* Harvey P. Dale, Oct 19 2024 *)
PROG
(Magma) [5*4^n+1: n in [0..30]];
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Nov 04 2011
STATUS
approved