cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A221910 a(n) = 8^n + 8*n.

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%I A221910 #31 Apr 12 2025 18:23:45
%S A221910 1,16,80,536,4128,32808,262192,2097208,16777280,134217800,1073741904,
%T A221910 8589934680,68719476832,549755813992,4398046511216,35184372088952,
%U A221910 281474976710784,2251799813685384,18014398509482128,144115188075856024,1152921504606847136,9223372036854775976
%N A221910 a(n) = 8^n + 8*n.
%H A221910 Vincenzo Librandi, <a href="/A221910/b221910.txt">Table of n, a(n) for n = 0..1000</a>
%H A221910 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (10,-17,8).
%F A221910 G.f.: (1+6*x-63*x^2)/((1-x)^2*(1-8*x)).
%F A221910 a(n) = 10*a(n-1) - 17*a(n-2) + 8*a(n-3).
%F A221910 E.g.f.: exp(x)*(exp(7*x) + 8*x). - _Elmo R. Oliveira_, Sep 10 2024
%t A221910 Table[(8^n + 8 n), {n, 0, 30}] (* or *) CoefficientList[Series[(1 + 6 x - 63 x^2)/((1 - x)^2(1 - 8 x)), {x, 0, 30}], x]
%t A221910 LinearRecurrence[{10,-17,8},{1,16,80},20] (* _Harvey P. Dale_, May 29 2021 *)
%o A221910 (Magma) [8^n + 8*n: n in [0..30]];
%o A221910 (Magma) I:=[1, 16, 80]; [n le 3 select I[n] else 10*Self(n-1)-17*Self(n-2)+8*Self(n-3): n in [1..30]];
%o A221910 (PARI) a(n)=8^n+8*n \\ _Charles R Greathouse IV_, Apr 18 2013
%Y A221910 Cf. A198398, A226201, A370661.
%K A221910 nonn,easy
%O A221910 0,2
%A A221910 _Vincenzo Librandi_, Mar 02 2013