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A001021 Powers of 12.
(Formerly M4869 N2084)
58
1, 12, 144, 1728, 20736, 248832, 2985984, 35831808, 429981696, 5159780352, 61917364224, 743008370688, 8916100448256, 106993205379072, 1283918464548864, 15407021574586368, 184884258895036416, 2218611106740436992 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
Same as Pisot sequences E(1, 12), L(1, 12), P(1, 12), T(1, 12). Essentially same as Pisot sequences E(12, 144), L(12, 144), P(12, 144), T(12, 144). See A008776 for definitions of Pisot sequences.
Central terms of the triangle in A100851. - Reinhard Zumkeller, Mar 04 2006
The compositions of n in which each natural number is colored by one of p different colors are called p-colored compositions of n. For n>=1, a(n) equals the number of 12-colored compositions of n such that no adjacent parts have the same color. - Milan Janjic, Nov 17 2011
Starting with 12, this sequence appears in the film "Vollmond" (1998, dir. Fredi Murer), when the children write it on the sidewalk at night. - Alonso del Arte, Dec 21 2011
A001222(a(n)) = A008585(n); A000005(a(n)) = A000384(a(n)). - Reinhard Zumkeller, Mar 31 2012
REFERENCES
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
P. J. Cameron, Sequences realized by oligomorphic permutation groups, J. Integ. Seqs. Vol. 3 (2000), #00.1.5.
Tanya Khovanova, Recursive Sequences
Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.
Simon Plouffe, 1031 Generating Functions, Appendix to Thesis, Montreal, 1992
Y. Puri and T. Ward, Arithmetic and growth of periodic orbits, J. Integer Seqs., Vol. 4 (2001), #01.2.1.
FORMULA
G.f.: 1/(1-12*x)
E.g.f.: exp(12x)
a(n) = 12*a(n-1). - Zerinvary Lajos, Apr 27 2009
a(n) = A159991(n)/A000351(n). - Reinhard Zumkeller, May 02 2009
a(n) = A000302(n) * A000244(n). - Reinhard Zumkeller, Mar 31 2012
a(n) = det(|ps(i+2, j)|, 1 <= i, j <= n), where ps(n, k) are Legendre-Stirling numbers of the first kind. - Mircea Merca, Apr 04 2013
MAPLE
A001021:=-1/(-1+12*z); # Simon Plouffe in his 1992 dissertation
MATHEMATICA
Table[12^n, {n, 0, 40}] (* Vladimir Joseph Stephan Orlovsky, Feb 15 2011 *)
PROG
(PARI) a(n)=12^n \\ Charles R Greathouse IV, Dec 21 2011
(Haskell)
a001021 = (12 ^)
a001021_list = iterate (* 12) 1 -- Reinhard Zumkeller, Mar 31 2012
CROSSREFS
Cf. A024140 and A178248, 12^n +/- 1; A016125, Expansion of 1/((1 - x)(1 - 12x)).
Sequence in context: A171286 A190132 A267791 * A159490 A245853 A000468
KEYWORD
nonn,easy
AUTHOR
STATUS
approved

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Last modified February 28 03:01 EST 2024. Contains 370379 sequences. (Running on oeis4.)