A258807 a(n) = n^5 - 1.
0, 31, 242, 1023, 3124, 7775, 16806, 32767, 59048, 99999, 161050, 248831, 371292, 537823, 759374, 1048575, 1419856, 1889567, 2476098, 3199999, 4084100, 5153631, 6436342, 7962623, 9765624, 11881375, 14348906, 17210367, 20511148, 24299999, 28629150, 33554431
Offset: 1
Links
- Muniru A Asiru, Table of n, a(n) for n = 1..5000
- Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).
Crossrefs
Programs
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GAP
List([1..35],n->n^5-1); # Muniru A Asiru, Oct 28 2018
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Magma
[n^5-1: n in [1..50]];
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Magma
I:=[0,31,242,1023, 3124,7775]; [n le 6 select I[n] else 6*Self(n-1)-15*Self(n-2)+20*Self(n-3)-15*Self(n-4)+ 6*Self(n-5)-Self(n-6): n in [1..50]];
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Maple
seq(n^5-1,n=1..35); # Muniru A Asiru, Oct 28 2018
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Mathematica
Table[n^5 - 1, {n, 1, 50}] (* or *) LinearRecurrence[{6, -15, 20, -15, 6, -1}, {0, 31, 242, 1023, 3124, 7775}, 50] -
PARI
a(n)=n^5-1 \\ Charles R Greathouse IV, Jun 11 2015
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Python
for n in range(1, 50): print(n**5 - 1, end=', ') # Stefano Spezia, Oct 28 2018
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Sage
[n^5-1 for n in (1..50)] # Bruno Berselli, Jun 11 2015
Formula
G.f.: x^2*(31 + 56*x + 36*x^2 - 4*x^3 + x^4)/(1 - x)^6.
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).
a(n) = -A024003(n). - Bruno Berselli, Jun 11 2015
Sum_{n>=2} 1/a(n) = Sum_{n>=1} (zeta(5*n) - 1) = 0.0379539032... - Amiram Eldar, Nov 06 2020