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A001023
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Powers of 14.
(Formerly M4949 N2120)
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10
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1, 14, 196, 2744, 38416, 537824, 7529536, 105413504, 1475789056, 20661046784, 289254654976, 4049565169664, 56693912375296, 793714773254144, 11112006825558016, 155568095557812224, 2177953337809371136, 30491346729331195904, 426878854210636742656, 5976303958948914397184, 83668255425284801560576
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| A000005(a(n)) = A000290(n+1). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Mar 04 2007
Number of n-permutations of 15 objects: l, m, n, o, p, q, r, s, t, u, v, w, z, x, y with repetition allowed and containing no u's, (u-free). Permutations with repetitions! If n=0 then 1 >>14^0=1 "". (no u's.) If n=1 then 13 >>14^1=14, >> l, m, n, o, p, q, r, s, t, v, w, z, x, y. (no u's.) etc. [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 01 2009]
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 14-colored compositions of n such that no adjacent parts have the same color. - Milan Janjic, Nov 17 2011
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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).
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LINKS
| T. D. Noe, Table of n, a(n) for n = 0..100
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 278
Tanya Khovanova, Recursive Sequences
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.
Y. Puri and T. Ward, Arithmetic and growth of periodic orbits, J. Integer Seqs., Vol. 4 (2001), #01.2.1.
Index to sequences with linear recurrences with constant coefficients, signature (14).
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FORMULA
| G.f.: 1/(1-14x), e.g.f.: exp(14x)
a(n) = 14^n; a(n) = 14*a(n-1) with a(0)=1. [From Vincenzo Librandi, Nov 21 2010]
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MAPLE
| A001023:=-1/(-1+14*z); [Conjectured by S. Plouffe in his 1992 dissertation.]
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MATHEMATICA
| Table[14^n, {n, 0, 40}] (*From Vladimir Joseph Stephan Orlovsky, Feb 15 2011*)
Denominator/@HermiteH[Range[0, 20], 5/28] (* From Harvey P. Dale, Jul 11 2011 *)
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PROG
| (Other) sage: [lucas_number1(n, 14, 0) for n in xrange(1, 18)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 29 2009]
(MAGMA) [ 14^n: n in [0..20] ]; [From Vincenzo Librandi, Nov 21 2010]
(MAGMA) [ n eq 1 select 1 else 14*Self(n-1): n in [1..21] ];
(PARI) a(n)=14^n \\ Charles R Greathouse IV, Nov 18 2011
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CROSSREFS
| C.f. A160193.
Sequence in context: A207120 A207074 A171288 * A067221 A072533 A041085
Adjacent sequences: A001020 A001021 A001022 * A001024 A001025 A001026
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from James A. Sellers (sellersj(AT)math.psu.edu), Sep 19 2000
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