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 A027441 a(n) = (n^4 + n)/2, (Row sums of an n X n X n magic cube, when it exists). 80
 0, 1, 9, 42, 130, 315, 651, 1204, 2052, 3285, 5005, 7326, 10374, 14287, 19215, 25320, 32776, 41769, 52497, 65170, 80010, 97251, 117139, 139932, 165900, 195325, 228501, 265734, 307342, 353655, 405015, 461776, 524304, 592977, 668185, 750330, 839826, 937099 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Starting with offset 1 = binomial transform of (1, 8, 25, 30, 12, 0, 0, 0,...). - Gary W. Adamson, May 20 2009 a(n) = sum(k: n<=k<=n^2); for n>0: a(n) = A037270(n) - A000217(n-1). - Reinhard Zumkeller, Jul 06 2010 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..680 Eric Weisstein's World of Mathematics, Magic Constant Eric Weisstein's World of Mathematics, Magic Cube Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1). FORMULA O.g.f.: x*(1+4*x+7*x^2)/(1-x)^5. - R. J. Mathar, Feb 13 2008 a(n) = 5*a(n-1)-10*a(n-2)+10*a(n-3)-5*a(n-4)+a(n-5). - Wesley Ivan Hurt, Aug 13 2014 a(n) = ( sum_{i=1..n^3} i ) / n^2, for n > 0. - Wesley Ivan Hurt, Aug 13 2014 a(n) = A002061(n)*A000217(n). - Anton Zakharov, Dec 16 2016 a(n) = (n+1)*(a(n-1)/(n-1) + n*(n-1)), a(0)=0, a(1)=1. - Vladimir Kruchinin, Oct 10 2018 MAPLE A027441:=n->(n^4+n)/2: seq(A027441(n), n=0..30); # Wesley Ivan Hurt, Aug 13 2014 MATHEMATICA Table[(n^4 + n)/2, {n, 0, 30}] (* Wesley Ivan Hurt, Aug 13 2014 *) LinearRecurrence[{5, -10, 10, -5, 1}, {0, 1, 9, 42, 130}, 40] (* Harvey P. Dale, Apr 09 2018 *) PROG (MAGMA) [(n^4+n)/2: n in [0..50]]; // Vincenzo Librandi, Apr 29 2011 (PARI) a(n)=(n^4 + n)/2 \\ Charles R Greathouse IV, Jul 28 2015 CROSSREFS Subsequence of A057590. Cf. A002061, A139562, A179268. Sequence in context: A062783 A172464 A269053 * A000971 A061927 A292481 Adjacent sequences:  A027438 A027439 A027440 * A027442 A027443 A027444 KEYWORD nonn,easy AUTHOR EXTENSIONS More terms from Wesley Ivan Hurt, Aug 13 2014 STATUS approved

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Last modified December 12 22:06 EST 2019. Contains 329963 sequences. (Running on oeis4.)