|
Search: id:A001025
|
|
|
| A001025 |
|
Powers of 16.
(Formerly M5021 N2164)
|
|
+0
20
|
|
| 1, 16, 256, 4096, 65536, 1048576, 16777216, 268435456, 4294967296, 68719476736, 1099511627776, 17592186044416, 281474976710656, 4503599627370496, 72057594037927936, 1152921504606846976, 18446744073709551616, 295147905179352825856, 4722366482869645213696, 75557863725914323419136, 1208925819614629174706176
(list; graph; listen)
|
|
|
OFFSET
|
0,2
|
|
|
COMMENT
|
Convolution-square (auto-convolution) of A098430. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 22 2009]
Subsequence of A161441: A160700(a(n)) = 1. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jun 10 2009]
|
|
REFERENCES
|
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
|
|
LINKS
|
S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
Tanya Khovanova, Recursive Sequences
Y. Puri and T. Ward, Arithmetic and growth of periodic orbits, J. Integer Seqs., Vol. 4 (2001), #01.2.1.
P. J. Cameron, Sequences realized by oligomorphic permutation groups, J. Integ. Seqs. Vol. 3 (2000), #00.1.5.
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 280
|
|
FORMULA
|
G.f.: 1/(1-16x), e.g.f.: exp(16x)
a(n)=2^(4n) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Aug 06 2009]
|
|
EXAMPLE
|
For n=0, a(0)=1; n=1, a(1)=16; n=2, a(2)=256 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Aug 06 2009]
|
|
MAPLE
|
A001025:=-1/(-1+16*z); [Conjectured by S. Plouffe in his 1992 dissertation.]
|
|
MATHEMATICA
|
lst={}; Do[AppendTo[lst, 16^n], {n, 0, 4!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Mar 01 2009]
|
|
PROGRAM
|
(Other) sage: [lucas_number1(n, 16, 0) for n in xrange(1, 18)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 29 2009]
|
|
CROSSREFS
|
Partial sums give A131865.
Sequence in context: A016744 A122609 A136577 this_sequence A144318 A067223 A041113
Adjacent sequences: A001022 A001023 A001024 this_sequence A001026 A001027 A001028
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
N. J. A. Sloane (njas(AT)research.att.com).
|
|
EXTENSIONS
|
More terms from Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Aug 06 2009
|
|
|
Search completed in 0.002 seconds
|
