A382612 a(n) = n^3 * (n^2 - n + 1).

0, 1, 24, 189, 832, 2625, 6696, 14749, 29184, 53217, 91000, 147741, 229824, 344929, 502152, 712125, 987136, 1341249, 1790424, 2352637, 3048000, 3898881, 4930024, 6168669, 7644672, 9390625, 11441976, 13837149, 16617664, 19828257, 23517000, 27735421, 32538624, 37985409, 44138392, 51064125, 58833216, 67520449, 77204904, 87970077, 99904000, 113099361, 127653624

Offset: 0

Author

Wesley Ivan Hurt, Mar 31 2025

Keywords

• easy
• nonn

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).

Examples

			                                                        [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
		

Links

• Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Crossrefs

Cf. A088020 (product of all entries).

Cf. A382532 (product along main antidiagonal).

Cf. A382620 (product along border).

Programs

Magma

[n^3*(n^2 - n + 1) : n in [0..50]]; // Wesley Ivan Hurt, Apr 15 2025

Mathematica

Table[n^3 (n^2 - n + 1), {n, 0, 60}]

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