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.

A275766 a(n) = (5^(2*(n + 1)) - 1)/4.

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%I A275766 #15 Aug 30 2016 04:18:12
%S A275766 156,3906,97656,2441406,61035156,1525878906,38146972656,953674316406,
%T A275766 23841857910156,596046447753906,14901161193847656,372529029846191406,
%U A275766 9313225746154785156,232830643653869628906,5820766091346740722656,145519152283668518066406
%N A275766 a(n) = (5^(2*(n + 1)) - 1)/4.
%C A275766 It seems that these terms are the only numbers n such that n and n + 1 are in A053696.
%H A275766 Colin Barker, <a href="/A275766/b275766.txt">Table of n, a(n) for n = 1..700</a>
%H A275766 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (26,-25).
%F A275766 a(n) = ((A125831(n+1))^3 - 1)/(A125831(n+1) - 1) - 1.
%F A275766 a(n) = A003463(2*(n+1)).
%F A275766 a(n) = 26*a(n-1) - 25*a(n-2), a(1) = 156, a(2) = 3906.
%F A275766 G.f.: 6*x*(26-25*x) / ((1-x)*(1-25*x)). - _Colin Barker_, Aug 24 2016
%e A275766 3906 written in base 5 is 111111 and 3907 written in base 62 is 111.
%t A275766 Table[(5^(2 (n + 1)) - 1)/4, {n, 16}] (* or *)
%t A275766 Rest@ CoefficientList[Series[6 x (26 - 25 x)/((1 - x) (1 - 25 x)), {x, 0, 16}], x] (* _Michael De Vlieger_, Aug 28 2016 *)
%o A275766 (PARI) Vec(6*x*(26-25*x)/((1-x)*(1-25*x)) + O(x^20)) \\ _Colin Barker_, Aug 24 2016
%o A275766 (PARI) a(n) = 5^(2*n+2)\4 \\ _Charles R Greathouse IV_, Aug 28 2016
%Y A275766 Cf. A003463, A053696, A125831.
%K A275766 nonn,easy
%O A275766 1,1
%A A275766 _Gionata Neri_, Aug 07 2016