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 A001621 a(n) = n*(n + 1)*(n^2 + n + 2)/4. 5
 0, 2, 12, 42, 110, 240, 462, 812, 1332, 2070, 3080, 4422, 6162, 8372, 11130, 14520, 18632, 23562, 29412, 36290, 44310, 53592, 64262, 76452, 90300, 105950, 123552, 143262, 165242, 189660, 216690, 246512, 279312, 315282, 354620, 397530, 444222, 494912, 549822 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Number of integer sequences of length n+1 with sum zero and sum of absolute values 4. - R. H. Hardin, Feb 22 2009 Partial sums of A034262. - Jeremy Gardiner, Jun 23 2013 LINKS T. D. Noe, Table of n, a(n) for n = 0..1000 FORMULA Equals 2 * A002817 and (A058919(n-1) - 1)/2. G.f.: (-2*x*(x^2+x+1))/(x-1)^5. - Maksym Voznyy (voznyy(AT)mail.ru), Jul 27 2009 a(n) = A000217(n) * A000124(n). - Torlach Rush, Aug 05 2018 MATHEMATICA a[n_]:=Sum[i+i^3, {i, 1, n}]; (* Vladimir Joseph Stephan Orlovsky, Dec 05 2008 *) Array[# (# + 1) (#^2 + # + 2)/4 &, 39, 0] (* or *) CoefficientList[Series[-2x (x^2 + x + 1)/(x - 1)^5, {x, 0, 38}], x] (* or *) LinearRecurrence[{5, -10, 10, -5, 1}, {0, 2, 12, 42, 110}, 39] (* Robert G. Wilson v, Aug 05 2018 *) CROSSREFS Cf. A002817, A058919, A092365. Sequence in context: A185619 A048014 A094702 * A277935 A290928 A232584 Adjacent sequences:  A001618 A001619 A001620 * A001622 A001623 A001624 KEYWORD nonn AUTHOR STATUS approved

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Last modified April 22 19:11 EDT 2021. Contains 343177 sequences. (Running on oeis4.)