A027482 a(n) = n*(n^3 - 1)/2.

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

Offset

2,1

Comments

Row sums in an n X n X n pandiagonal magic cube with entries (0..n^3-1).

Links

Vincenzo Librandi, Table of n, a(n) for n = 2..1000

S. Gartenhaus, Odd order pandiagonal latin and magic cubes in three and four dimensions, arXiv:math/0210275 [math.CO], 2002.

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

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: A329528 A215441 A373539 * A352310 A196782 A128554

Adjacent sequences: A027479 A027480 A027481 * A027483 A027484 A027485

Keyword

nonn,easy

Author

Olivier Gérard

Status

approved