OFFSET
2,1
COMMENTS
Decimal form of the hexadecimal numbers 2, 22, 222, 2222, 22222, 222222, ...; e.g., 2*16^0 + 2*16^1 = 2 + 32 = 34. - Zerinvary Lajos, Feb 01 2007
For n>0: A131852(a(n+1))=n and ABS(A131852(m))<n for m<a(n+1); a(n)=2*A131865(n-2). - Reinhard Zumkeller, Jul 22 2007
Third quadrisection of A115451. - Klaus Purath, Mar 14 2021
LINKS
Harvey P. Dale, Table of n, a(n) for n = 2..832
Index entries for linear recurrences with constant coefficients, signature (17,-16).
FORMULA
lim_{n -> infinity} a(n)/a(n-k) = 2^(4*(n-k)).
2*Sum_{k=0..n} 16^k = 2*(16^(n+1) - 1)/15.
From Klaus Purath, Mar 14 2021: (Start)
a(n) = (2^(4*n-3)-2)/15.
a(n) = 17*a(n-1) - 16*a(n-2).
a(n) = 16*a(n-1) + 2.
a(n) = 2*16^(n-2) + a(n-1).
a(n) = 2*A131865(n-2). (End)
MATHEMATICA
s=0; lst={}; Do[s+=2^n; AppendTo[lst, s], {n, 1, 2*5!, 4}]; lst (* Vladimir Joseph Stephan Orlovsky, Nov 07 2008 *)
FromDigits[#, 2]&/@Table[Join[PadRight[{}, 4n, {1, 0, 0, 0}], {1, 0}], {n, 0, 20}] (* Harvey P. Dale, Apr 06 2020 *)
PROG
(PARI) for(n=0, 20, print(2*sum(k=0, n, 2^(4*k))))
for(k=0, 20, print(2*(1-16^(k+1))/-15))
CROSSREFS
KEYWORD
nonn,base,easy
AUTHOR
Simone Severini, Oct 26 2004
EXTENSIONS
More terms from Ray Chandler, Nov 02 2004
More terms from Vladimir Joseph Stephan Orlovsky, Nov 07 2008
STATUS
approved