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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).

%I A027441 #66 Mar 11 2025 15:44:45
%S A027441 0,1,9,42,130,315,651,1204,2052,3285,5005,7326,10374,14287,19215,
%T A027441 25320,32776,41769,52497,65170,80010,97251,117139,139932,165900,
%U A027441 195325,228501,265734,307342,353655,405015,461776,524304,592977,668185,750330,839826,937099
%N A027441 a(n) = (n^4 + n)/2 (Row sums of an n X n X n magic cube, when it exists).
%C A027441 Starting with offset 1 = binomial transform of (1, 8, 25, 30, 12, 0, 0, 0, ...). - _Gary W. Adamson_, May 20 2009
%H A027441 Kelvin Voskuijl, <a href="/A027441/b027441.txt">Table of n, a(n) for n = 0..10000</a> (terms 0-680 by Vincenzo Librandi.)
%H A027441 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MagicConstant.html">Magic Constant</a>
%H A027441 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MagicCube.html">Magic Cube</a>
%H A027441 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F A027441 O.g.f.: x*(1+4*x+7*x^2)/(1-x)^5. - _R. J. Mathar_, Feb 13 2008
%F A027441 a(n) = Sum_{k=n..n^2} k; for n>0: a(n) = A037270(n) - A000217(n-1). - _Reinhard Zumkeller_, Jul 06 2010
%F A027441 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
%F A027441 a(n) = A071232(n) / n^2, for n > 0. - _Wesley Ivan Hurt_, Aug 13 2014
%F A027441 a(n) = A002061(n)*A000217(n). - _Anton Zakharov_, Dec 16 2016
%F A027441 a(n) = (n+1)*(a(n-1)/(n-1) + n*(n-1)), a(0)=0, a(1)=1. - _Vladimir Kruchinin_, Oct 10 2018
%p A027441 A027441:=n->(n^4+n)/2: seq(A027441(n), n=0..30); # _Wesley Ivan Hurt_, Aug 13 2014
%t A027441 Table[(n^4 + n)/2, {n, 0, 30}] (* _Wesley Ivan Hurt_, Aug 13 2014 *)
%t A027441 LinearRecurrence[{5,-10,10,-5,1},{0,1,9,42,130},40] (* _Harvey P. Dale_, Apr 09 2018 *)
%o A027441 (Magma) [(n^4+n)/2: n in [0..50]]; // _Vincenzo Librandi_, Apr 29 2011
%o A027441 (PARI) a(n)=(n^4 + n)/2 \\ _Charles R Greathouse IV_, Jul 28 2015
%Y A027441 Subsequence of A057590.
%Y A027441 Cf. A002061, A139562, A179268.
%K A027441 nonn,easy
%O A027441 0,3
%A A027441 _Eric W. Weisstein_
%E A027441 More terms from _Wesley Ivan Hurt_, Aug 13 2014