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A027482 a(n) = n*(n^3 - 1)/2. 3
7, 39, 126, 310, 645, 1197, 2044, 3276, 4995, 7315, 10362, 14274, 19201, 25305, 32760, 41752, 52479, 65151, 79990, 97230, 117117, 139909, 165876, 195300, 228475, 265707, 307314, 353626, 404985, 461745, 524272, 592944, 668151 (list; graph; refs; listen; history; text; internal format)
OFFSET
2,1
COMMENTS
Row sums in an n X n X n pandiagonal magic cube with entries (0..n^3-1).
LINKS
S. Gartenhaus, Odd order pandiagonal latin and magic cubes in three and four dimensions, arXiv:math/0210275 [math.CO], 2002.
FORMULA
a(n) = A027478(n,n-1)
a(n) = A000217(n^2) - A000217(n). - Jon Perry, Jul 21 2003
a(n) = A058895(n)/2. - Zerinvary Lajos, Jan 28 2008
G.f.: x^2*(7 + 4*x + x^2)/(1 - x)^5. - Vincenzo Librandi, Dec 29 2012
a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n > 6. - Chai Wah Wu, Apr 08 2021
MATHEMATICA
Table[(m^4 - m)/2, {m, 44}] (* Zerinvary Lajos, Mar 21 2007 *)
CoefficientList[Series[(7 + 4*x + x^2)/(1 - x)^5, {x, 0, 40}], x] (* Vincenzo Librandi, Dec 29 2012 *)
PROG
(PARI) t(n)=n*(n+1)/2;
for(n=0, 50, print1(t(n^2)-t(n)", "))
(Magma) [n * (n^3 - 1)/2: n in [2..50]]; // Vincenzo Librandi, Dec 29 2012
CROSSREFS
First subdiagonal of A027478 (Cube of a triangular matrix constructed from the Stirling numbers of the first kind).
Sequence in context: A304012 A329528 A215441 * A352310 A196782 A128554
KEYWORD
nonn,easy
AUTHOR
STATUS
approved

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Last modified March 29 05:48 EDT 2024. Contains 371265 sequences. (Running on oeis4.)