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 A005912 Truncated cube numbers. (Formerly M5312) 2
 1, 56, 311, 920, 2037, 3816, 6411, 9976, 14665, 20632, 28031, 37016, 47741, 60360, 75027, 91896, 111121, 132856, 157255, 184472, 214661, 247976, 284571, 324600, 368217, 415576, 466831, 522136, 581645, 645512, 713891, 786936, 864801, 947640, 1035607, 1128856 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 REFERENCES N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Reinhard Zumkeller, Table of n, a(n) for n = 0..10000 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 B. K. Teo and N. J. A. Sloane, Magic numbers in polygonal and polyhedral clusters, Inorgan. Chem. 24 (1985), 4545-4558. Index entries for linear recurrences with constant coefficients, signature (4, -6, 4, -1). FORMULA a(n) = (3*n+1)^3 - 8*(n)*(n+1)*(n+2)/6 = (77/3)*n^3 + 23*n^2 + (19/3)*n + 1. a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4); a(0)=1, a(1)=56, a(2)=311, a(3)=920. - Harvey P. Dale, Aug 14 2011 MAPLE A005912:=(1+52*z+93*z**2+8*z**3)/(z-1)**4; # conjectured by Simon Plouffe in his 1992 dissertation MATHEMATICA Table[(3n+1)^3-8(n)(n+1)(n+2)/6, {n, 0, 30}] (* or *) LinearRecurrence[ {4, -6, 4, -1}, {1, 56, 311, 920}, 30] (* Harvey P. Dale, Aug 14 2011 *) PROG (Haskell) a005912 n = (n * (n * (77 * n + 69) + 19) + 3) `div` 3 :: Integer -- Reinhard Zumkeller, Aug 09 2014 (Magma) [(3*n+1)^3-8*(n)*(n+1)*(n+2)/6: n in [0..40]] // Vincenzo Librandi, Aug 09 2014 (PARI) a(n)=(3*n+1)^3-8*(n)*(n+1)*(n+2)/6 \\ Charles R Greathouse IV, Feb 10 2017 CROSSREFS Sequence in context: A110554 A253922 A220015 * A264581 A220202 A104677 Adjacent sequences: A005909 A005910 A005911 * A005913 A005914 A005915 KEYWORD nonn,easy,nice AUTHOR N. J. A. Sloane EXTENSIONS More terms from Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Dec 22 1999 STATUS approved

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Last modified December 9 16:37 EST 2023. Contains 367693 sequences. (Running on oeis4.)