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