A024121 a(n) = 10^n - n^7.
1, 9, -28, -1187, -6384, 21875, 720064, 9176457, 97902848, 995217031, 9990000000, 99980512829, 999964168192, 9999937251483, 99999894586496, 999999829140625, 9999999731564544, 99999999589661327, 999999999387779968
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..300
- Index entries for linear recurrences with constant coefficients, signature (18,-108,336,-630,756,-588,288,-81,10).
Programs
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GAP
List([0..20],n->10^n-n^7); # Muniru A Asiru, Oct 16 2018
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Magma
[10^n-n^7: n in [0..20]]; // Vincenzo Librandi, Jul 01 2011
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Maple
seq(10^n-n^7,n=0..20); # Muniru A Asiru, Oct 16 2018
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Mathematica
a[n_]:=10^n - n^7; Array[a, 50, 0] (* Stefano Spezia, Oct 04 2018 *) LinearRecurrence[{18,-108,336,-630,756,-588,288,-81,10},{1,9,-28,-1187,-6384,21875,720064,9176457,97902848},20] (* Harvey P. Dale, Sep 16 2021 *)
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PARI
a(n)=10^n-n^7 \\ Charles R Greathouse IV, Jul 01 2011
Formula
From Stefano Spezia, Oct 04 2018: (Start)
a(n) = 18*a(n - 1) - 108*a(n - 2) + 336*a(n - 3) - 630*a(n - 4) + 756*a(n - 5) - 588*a(n - 6) + 288*a(n - 7) - 81*a(n - 8) + 10*a(n - 9) for n > 8.
G.f.: -((1 - 9*x - 82*x^2 - 47*x^3 + 9564*x^4 + 22913*x^5 + 11818*x^6 + 1191*x^7 + 11*x^8)/((-1 + x)^8*(-1 + 10*x))).
E.g.f.: exp(x)*(exp(9*x) - x - 63*x^2 - 301*x^3 - 350*x^4 - 140*x^5 - 21*x^6 - x^7).
(End)