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A022521
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Nexus numbers (n+1)^5-n^5.
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14
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1, 31, 211, 781, 2101, 4651, 9031, 15961, 26281, 40951, 61051, 87781, 122461, 166531, 221551, 289201, 371281, 469711, 586531, 723901, 884101, 1069531, 1282711, 1526281, 1803001, 2115751, 2467531
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Last digit of a(n) is always 1. Last two digits of a(n) Mod[a(n),100] are repeated periodically with palindromic period of length 20 {1,31,11,81,1,51,31,61,81,51,51,81,61,31,51,1,81,11,31,1}. Last three digits of a(n) Mod[a(n),1000] are repeated periodically with palindromic period of length 200. - Alexander Adamchuk (alex(AT)kolmogorov.com), Aug 11 2006
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REFERENCES
| J. H. Conway and R. K. Guy, The Book of Numbers, p. 54.
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Index entries for sequences related to linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
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FORMULA
| Sequence is 24*0+1, 24*1+7, 24*8+19, 24*31+37, ... a(n) = [1+sum(6*n)]+ 24*[sum(sum(1+sum(5*n)))] or a(n)= A003215 + 24 * A006322 or a(n)= [n^3-(n-1)^3]+24*[sum(sum(1+sum(5*n)))] - Xavier Acloque Oct 11 2003
G.f.:(-1-x^4-26*x^3-66*x^2-26*x)/(x-1)^5 [From Maksym Voznyy (voznyy(AT)mail.ru), Aug 11 2009]
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MATHEMATICA
| q=5; lst={}; Do[AppendTo[lst, (n+1)^q-n^q], {n, 0, 5!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Jan 23 2009]
Table[(n+1)^5-n^5, {n, 0, 30} (* Vincenzo Librandi, Nov 23 2011 *)
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PROG
| (MAGMA) [(n+1)^5-n^5: n in [0..30]]; // Vincenzo Librandi, Nov 23 2011
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CROSSREFS
| First differences of A000584. A row of A047969.
Sequence in context: A096906 A181124 A142328 * A152730 A090027 A164784
Adjacent sequences: A022518 A022519 A022520 * A022522 A022523 A022524
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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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