|
|
A070302
|
|
Number of 3 X 3 X 3 magic cubes with sum 3n.
|
|
3
|
|
|
1, 19, 121, 439, 1171, 2581, 4999, 8821, 14509, 22591, 33661, 48379, 67471, 91729, 122011, 159241, 204409, 258571, 322849, 398431, 486571, 588589, 705871, 839869, 992101, 1164151, 1357669, 1574371, 1816039, 2084521, 2381731, 2709649
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
LINKS
|
D. C. Haws, Matroids [Broken link, Oct 30 2017]
D. C. Haws, Matroids [Copy on website of Matthias Koeppe]
|
|
FORMULA
|
G.f.: x*(x^4 + 14x^3 + 36x^2 + 14x + 1)/(1 - x)^5. [corrected by R. J. Mathar, Jan 26 2010]
a(n) = 25*n^2/4 - 7*n/2 - 11*n^3/2 + 11*n^4/4 + 1. - R. J. Mathar, Sep 04 2011
Sum_{n>=1} 1/a(n) = 2*Pi*(sqrt(17 + 4*sqrt(5)) * tanh(sqrt(17/44 - sqrt(5)/11)*Pi) - sqrt(17 - 4*sqrt(5))*tanh(sqrt(17/44 + sqrt(5)/11)*Pi)) / sqrt(95). - Vaclav Kotesovec, May 01 2018
|
|
MAPLE
|
seq(25*n^2/4-7*n/2-11*n^3/2+11*n^4/4+1, n=1..40); # Muniru A Asiru, Apr 30 2018
|
|
MATHEMATICA
|
Select[ CoefficientList[ Series[ (x^12 + 14x^9 + 36x^6 + 14x^3 + 1) / (1 - x^3)^5, {x, 0, 105}], x], # > 0 & ]
(* Second program: *)
LinearRecurrence[{5, -10, 10, -5, 1}, {1, 19, 121, 439, 1171}, 32] (* Jean-François Alcover, Jan 07 2019 *)
|
|
PROG
|
(Magma) [25*n^2/4 -7*n/2 -11*n^3/2 +11*n^4/4+1: n in [1..40]]; // Vincenzo Librandi, Sep 05 2011
(PARI) for(n=1, 30, print1(25*n^2/4 -7*n/2 -11*n^3/2 +11*n^4/4+1, ", ")) \\ G. C. Greubel, Apr 29 2018
(GAP) List([1..40], n->25*n^2/4-7*n/2-11*n^3/2+11*n^4/4+1); # Muniru A Asiru, Apr 30 2018
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
Sharon Sela (sharonsela(AT)hotmail.com), May 10 2002
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|