A027441 a(n) = (n^4 + n)/2 (Row sums of an n X n X n magic cube, when it exists).
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
Offset: 0
Links
- Kelvin Voskuijl, Table of n, a(n) for n = 0..10000 (terms 0-680 by Vincenzo Librandi.)
- 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).
Programs
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Magma
[(n^4+n)/2: n in [0..50]]; // Vincenzo Librandi, Apr 29 2011
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Maple
A027441:=n->(n^4+n)/2: seq(A027441(n), n=0..30); # Wesley Ivan Hurt, Aug 13 2014
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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 *) -
PARI
a(n)=(n^4 + n)/2 \\ Charles R Greathouse IV, Jul 28 2015
Formula
O.g.f.: x*(1+4*x+7*x^2)/(1-x)^5. - R. J. Mathar, Feb 13 2008
a(n) = Sum_{k=n..n^2} k; for n>0: a(n) = A037270(n) - A000217(n-1). - Reinhard Zumkeller, Jul 06 2010
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) = A071232(n) / n^2, for n > 0. - Wesley Ivan Hurt, Aug 13 2014
a(n) = (n+1)*(a(n-1)/(n-1) + n*(n-1)), a(0)=0, a(1)=1. - Vladimir Kruchinin, Oct 10 2018
Extensions
More terms from Wesley Ivan Hurt, Aug 13 2014
Comments