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 A034262 a(n) = n^3 + n. 30
 0, 2, 10, 30, 68, 130, 222, 350, 520, 738, 1010, 1342, 1740, 2210, 2758, 3390, 4112, 4930, 5850, 6878, 8020, 9282, 10670, 12190, 13848, 15650, 17602, 19710, 21980, 24418, 27030, 29822, 32800, 35970, 39338, 42910, 46692, 50690, 54910 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS k such that x^3 + x + k factors over the integers. - James R. Buddenhagen, Apr 19 2005 If a(n)=X [A155977], Y=b(n) [A071253], Z=c(n) [A034262], then X^2+Y^2 = n*Z^3; e.g., if n=3, a(3)=270, b(3)=90, c(3)=30, then 270^2+90^2=3*30^3. - Vincenzo Librandi, Nov 24 2010 From Bruno Berselli, Sep 06 2018: (Start) After 0, sum of next n even numbers: ... 2,                           2 ... 4,  6,                      10 ... 8, 10, 12,                  30 .. 14, 16, 18, 20,              68 .. 22, 24, 26, 28, 30,         130 .. 32, 34, 36, 38, 40, 42,     222 etc. (End) Sequence occurs in the binomial identity Sum_{k = 0..n} a(k)* binomial(n,k)/binomial(n+k,k) = n*(n + 1)/2. Cf. A092181 and A155977. - Peter Bala, Feb 12 2019 LINKS Reinhard Zumkeller, Table of n, a(n) for n = 0..10000 FORMULA a(n) = 2*A006003(n). a(n) = A002522(n)*A001477(n). - Zerinvary Lajos, Apr 20 2008 For n>1, a(n) = floor(n^5/(n^2-1)). - Gary Detlefs, Feb 10 2010 Sum_{n>=1} 1/a(n) = 0.6718659855... = gamma + Re psi(1+i) = A001620+A248117. [Borwein et al., J. Math. Anal. Appl. 316 (2006) 328]. - R. J. Mathar, Jul 17 2012 a(n) = -a(-n) for all n in Z. - Michael Somos, Jul 11 2017 MATHEMATICA Table[n^3 + n, {n, 0, 40}] (* Vladimir Joseph Stephan Orlovsky, Mar 06 2010 *) PROG (Haskell) a034262 n = a000578 n + n  -- Reinhard Zumkeller, Sep 26 2014 (PARI) {a(n) = n^3 + n}; /* Michael Somos, Jul 11 2017 */ CROSSREFS Cf. A001477, A002522. Cf. A000290, A001477. Cf. A071253, A155977. Cf. A001621. Cf. A000578. Sequence in context: A290461 A162524 A065137 * A180499 A167214 A034827 Adjacent sequences:  A034259 A034260 A034261 * A034263 A034264 A034265 KEYWORD nonn,easy,changed AUTHOR Stuart M. Ellerstein (ellerstein(AT)aol.com), Apr 21 2000 STATUS approved

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Last modified October 23 17:32 EDT 2019. Contains 328373 sequences. (Running on oeis4.)