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 A022521 a(n) = (n+1)^5 - n^5. 25
 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; text; internal format)
 OFFSET 0,2 COMMENTS Last digit of a(n) is always 1. Last two digits of a(n) (i.e., a(n) mod 100) are repeated periodically with palindromic part of period 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) (i.e., a(n) mod 1000) are repeated periodically with palindromic part of period 200. - Alexander Adamchuk, Aug 11 2006 In Conway and Guy, these numbers are called nexus numbers of order 5. - M. F. Hasler, Jan 27 2013 Numbers that can be arranged in a triangular-antitegmatic icosachoron (the 4D version of "rhombic dodecahedal numbers" (A005917)). - Steven Lu, Mar 28 2023 REFERENCES John H. Conway and Richard K. Guy, The Book of Numbers, Copernicus Press, NY, 1996, p. 54. LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..10000 Polytope Wiki, Triangular-antitegmatic Icosachoron Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1). FORMULA a(n) = A003215(n) + 24 * A006322(n). - Xavier Acloque, Oct 11 2003 G.f.: (-1-x^4-26*x^3-66*x^2-26*x)/(x-1)^5. - Maksym Voznyy (voznyy(AT)mail.ru), Aug 11 2009 G.f.: polylog(-5, x)*(1-x)/x. See the g.f. of the rows of A008292 by Vladeta Jovovic, Sep 02 2002. - Wolfdieter Lang, May 10 2021 Sum_{n>=0} 1/a(n) = c1*tanh(c2/2) - c2*tanh(c1/2), where c1 = tan(3*Pi/10)*Pi and c2 = tan(Pi/10)*Pi. - Amiram Eldar, Jan 27 2022 MATHEMATICA Table[(n+1)^5-n^5, {n, 0, 30}] (* Vincenzo Librandi, Nov 23 2011 *) PROG (Magma) [(n+1)^5-n^5: n in [0..30]]; // Vincenzo Librandi, Nov 23 2011 (PARI) a(n)=(n+1)^5-n^5 \\ Charles R Greathouse IV, Sep 24 2015 CROSSREFS First differences of A000584. Column k=4 of array A047969. Cf. A003215, A005917, A006322, A008292, A019916, A019952, A022522. Sequence in context: A096906 A181124 A142328 * A152730 A361700 A090027 Adjacent sequences: A022518 A022519 A022520 * A022522 A022523 A022524 KEYWORD nonn,easy AUTHOR N. J. A. Sloane STATUS approved

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Last modified June 9 14:59 EDT 2023. Contains 363181 sequences. (Running on oeis4.)