OFFSET
0,3
COMMENTS
Product of the entries in the corners of an n X n square array with elements 1..n^2 listed in increasing order by rows (see example).
LINKS
Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).
FORMULA
G.f.: x*(1+18*x+60*x^2+38*x^3+3*x^4)/(x-1)^6. - R. J. Mathar, Apr 02 2025
a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6). - Wesley Ivan Hurt, Apr 15 2025
EXAMPLE
[1 2 3 4 5]
[1 2 3 4] [6 7 8 9 10]
[1 2 3] [5 6 7 8] [11 12 13 14 15]
[1 2] [4 5 6] [9 10 11 12] [16 17 18 19 20]
[1] [3 4] [7 8 9] [13 14 15 16] [21 22 23 24 25]
------------------------------------------------------------------------
n 1 2 3 4 5
------------------------------------------------------------------------
1 1*2*3*4 1*3*7*9 1*4*13*16 1*5*21*25
------------------------------------------------------------------------
a(n) 1 24 189 832 2625
MATHEMATICA
Table[n^3 (n^2 - n + 1), {n, 0, 60}]
PROG
(Magma) [n^3*(n^2 - n + 1) : n in [0..50]]; // Wesley Ivan Hurt, Apr 15 2025
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Wesley Ivan Hurt, Mar 31 2025
STATUS
approved