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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). 83
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..n^2); for n>0: a(n) = A037270(n) - A000217(n-1). - Reinhard Zumkeller, Jul 06 2010
LINKS
Eric Weisstein's World of Mathematics, Magic Constant
Eric Weisstein's World of Mathematics, Magic Cube
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.
Sequence in context: A062783 A172464 A269053 * A000971 A061927 A292481
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
More terms from Wesley Ivan Hurt, Aug 13 2014
STATUS
approved

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Last modified March 19 03:21 EDT 2024. Contains 370952 sequences. (Running on oeis4.)