A123868 a(n) = n^12 - 1.
0, 4095, 531440, 16777215, 244140624, 2176782335, 13841287200, 68719476735, 282429536480, 999999999999, 3138428376720, 8916100448255, 23298085122480, 56693912375295, 129746337890624, 281474976710655, 582622237229760, 1156831381426175, 2213314919066160
Offset: 1
Links
- T. D. Noe, Table of n, a(n) for n = 1..1000
- Index entries for linear recurrences with constant coefficients, signature (13,-78,286,-715,1287,-1716,1716,-1287,715,-286,78,-13,1).
Programs
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GAP
List([1..20], n-> n^12 -1); # G. C. Greubel, Aug 08 2019
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Magma
[n^12 -1:n in [1..20]]; // Vincenzo Librandi, Dec 27 2010
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Maple
seq(n^(12) -1, n=1..20); # G. C. Greubel, Aug 08 2019
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Mathematica
Range[20]^12 -1 (* G. C. Greubel, Aug 08 2019 *)
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PARI
vector(20, n, n^12 -1) \\ G. C. Greubel, Aug 08 2019
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Sage
[n^12 -1 for n in (1..20)] # G. C. Greubel, Aug 08 2019
Formula
From Chai Wah Wu, Jun 18 2016: (Start)
a(n) = 13*a(n-1) - 78*a(n-2) + 286*a(n-3) - 715*a(n-4) + 1287*a(n-5) - 1716*a(n-6) + 1716*a(n-7) - 1287*a(n-8) + 715*a(n-9) - 286*a(n-10) + 78*a(n-11) - 13*a(n-12) + a(n-13) for n > 12.
G.f.: x*(4095 + 478205*x + 10187905*x^2 + 66317979*x^3 + 162513078*x^4 + 162511362*x^5 + 66319266*x^6 + 10187190*x^7 + 478491*x^8 + 4017*x^9 + 13*x^10 - x^11)/(1 - x)^13. (End)
Comments