cp's OEIS Frontend

A258806 a(n) = n^7 + 1.

%I A258806 #33 Jan 09 2025 14:52:00
%S A258806 1,2,129,2188,16385,78126,279937,823544,2097153,4782970,10000001,
%T A258806 19487172,35831809,62748518,105413505,170859376,268435457,410338674,
%U A258806 612220033,893871740,1280000001,1801088542,2494357889,3404825448,4586471425,6103515626,8031810177
%N A258806 a(n) = n^7 + 1.
%H A258806 Muniru A Asiru, <a href="/A258806/b258806.txt">Table of n, a(n) for n = 0..5000</a>
%H A258806 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (8,-28,56,-70,56,-28,8,-1).
%F A258806 G.f.: (1 - 6*x + 141*x^2 + 1156*x^3 + 2451*x^4 + 1170*x^5 + 127*x^6)/(1 - x)^8.
%F A258806 a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8).
%F A258806 a(n) = (n + 1)*(n^6 - n^5 + n^4 - n^3 + n^2 - n + 1).
%F A258806 a(n) = Sum_{k=0..n} A300785(n,k). - _Kolosov Petro_, Oct 23 2018
%F A258806 E.g.f.: (1 +x +63*x^2 +301*x^3 +350*x^4 +140*x^5 +*21*x^6 +x^7)*exp(x). - _G. C. Greubel_, Oct 24 2018
%p A258806 seq(n^7+1,n=0..30); # _Muniru A Asiru_, Oct 24 2018
%t A258806 Table[n^7 + 1, {n, 0, 40}] (* or *) LinearRecurrence[{8, -28, 56, -70, 56, -28, 8, -1}, {1, 2, 129, 2188, 16385, 78126, 279937, 823544}, 40]
%o A258806 (Magma) [n^7+1: n in [0..40]];
%o A258806 (Magma) I:=[1,2,129,2188, 16385,78126,279937,823544]; [n le 8 select I[n] else 8*Self(n-1) - 28*Self(n-2)+56*Self(n-3)-70*Self(n-4)+56*Self(n-5) -28*Self(n-6) + 8*Self(n-7)-Self(n-8): n in [1..40]];
%o A258806 (Sage) [n^7+1 for n in (1..40)] # _Bruno Berselli_, Jun 11 2015
%o A258806 (PARI) a(n)=n^7+1 \\ _Charles R Greathouse IV_, Jun 11 2015
%o A258806 (GAP) List([0..30],n->n^7+1); # _Muniru A Asiru_, Oct 24 2018
%Y A258806 Subsequence of A004864.
%Y A258806 Sequences of the type n^k+1: A002522 (k=2), A001093 (k=3), A002523 (k=4), A002561 (k=5), A002604 (k=6), this sequence (k=7), A060890 (k=8).
%Y A258806 Cf. A300785.
%K A258806 nonn,easy
%O A258806 0,2
%A A258806 _Vincenzo Librandi_, Jun 11 2015