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A001016
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Eighth powers: a(n) = n^8.
(Formerly M5426 N2357)
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48
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0, 1, 256, 6561, 65536, 390625, 1679616, 5764801, 16777216, 43046721, 100000000, 214358881, 429981696, 815730721, 1475789056, 2562890625, 4294967296, 6975757441, 11019960576, 16983563041, 25600000000, 37822859361, 54875873536, 78310985281, 110075314176
(list;
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refs;
listen;
history;
text;
internal format)
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OFFSET
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0,3
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COMMENTS
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Besides the first term, this sequence is the denominator of ((Pi)^8)/9450 = 1+1/256+1/6561+1/65536+1/390625+1/1679616+... - Mohammad K. Azarian, Nov 01 2011
For n > 0, a(n) is the largest number k such that k + n^4 divides k^2 + n^4. - Derek Orr, Oct 01 2014
Fourth powers of squares and squares of 4th powers. Squares composed with themselves twice. - Wesley Ivan Hurt, Apr 01 2016
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REFERENCES
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Granino A. Korn and Theresa M. Korn, Mathematical Handbook for Scientists and Engineers, McGraw-Hill Book Company, New York (1968), p. 982.
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
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T. D. Noe, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).
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FORMULA
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Multiplicative with a(p^e) = p^(8e). - David W. Wilson, Aug 01 2001
Totally multiplicative sequence with a(p) = p^8 for primes p. - Jaroslav Krizek, Nov 01 2009
G.f.: -x*(1+x)*(x^6+246*x^5+4047*x^4+11572*x^3+4047*x^2+246*x+1)/(x-1)^9. - R. J. Mathar, Jan 07 2011
a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) + 40320. - Ant King, Sep 24 2013
From Wesley Ivan Hurt, Apr 01 2016: (Start)
a(n) = 9*a(n-1)-36*a(n-2)+84*a(n-3)-126*a(n-4)+126*a(n-5)-84*a(n-6)+36*a(n-7)-9*a(n-8)+a(n-9) for n>8.
a(n) = A000290(n)^4 = A000290(A000290(A000290(n))).
a(n) = A000583(n)^2. (End)
From Amiram Eldar, Oct 08 2020: (Start)
Sum_{n>=1} 1/a(n) = zeta(8) = Pi^8/9450 (A013666).
Sum_{n>=1} (-1)^(n+1)/a(n) = 127*zeta(8)/128 = 127*Pi^8/1209600. (End)
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MAPLE
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A001016:=n->n^8: seq(A001016(n), n=0..50); # Wesley Ivan Hurt, Apr 01 2016
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MATHEMATICA
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Table[n^8, {n, 0, 20}] (* Vladimir Joseph Stephan Orlovsky, Sep 27 2008 *)
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PROG
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(Maxima) A001016(n):=n^8$
makelist(A001016(n), n, 0, 30); /* Martin Ettl, Nov 05 2012 */
(PARI) a(n)=n^8 \\ Charles R Greathouse IV, Sep 24 2015
(MAGMA) [n^8 : n in [0..50]]; // Wesley Ivan Hurt, Apr 01 2016
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CROSSREFS
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Cf. A000290 (squares), A000583 (fourth powers), A013666.
Sequence in context: A016900 A017680 A210840 * A050755 A046457 A179645
Adjacent sequences: A001013 A001014 A001015 * A001017 A001018 A001019
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KEYWORD
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nonn,easy,mult
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AUTHOR
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N. J. A. Sloane
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EXTENSIONS
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More terms from James A. Sellers, Sep 19 2000
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STATUS
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approved
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