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A176974 First exponent n to generate maximum remainder when (a + 1)^n + (a - 1)^n is divided by a^2 for variable n and a>2.

%I A176974 #14 Feb 21 2020 20:13:27
%S A176974 1,1,7,5,3,3,13,9,5,5,19,13,7,7,25,17,9,9,31,21,11,11,37,25,13,13,43,
%T A176974 29,15,15,49,33,17,17,55,37,19,19,61,41,21,21,67,45,23,23,73,49,25,25,
%U A176974 79,53,27,27,85,57,29,29,91,61,31,31,97,65,33,33,103,69
%N A176974 First exponent n to generate maximum remainder when (a + 1)^n + (a - 1)^n is divided by a^2 for variable n and a>2.
%H A176974 Colin Barker, <a href="/A176974/b176974.txt">Table of n, a(n) for n = 3..1000</a>
%H A176974 Project Euler, <a href="https://projecteuler.net/index.php?section=problems&amp;id=120">Problem 120: Square remainders</a>
%H A176974 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,2,0,0,0,-1).
%F A176974 From _Colin Barker_, Oct 29 2017: (Start)
%F A176974 G.f.: x^3*(1 + x + 7*x^2 + 5*x^3 + x^4 + x^5 - x^6 - x^7) / ((1 - x)^2*(1 + x)^2*(1 + x^2)^2).
%F A176974 a(n) = 2*a(n-4) - a(n-8) for n>10.
%F A176974 (End)
%o A176974 (PARI) Vec(x^3*(1 + x + 7*x^2 + 5*x^3 + x^4 + x^5 - x^6 - x^7) / ((1 - x)^2*(1 + x)^2*(1 + x^2)^2) + O(x^100)) \\ _Colin Barker_, Oct 29 2017
%Y A176974 Cf. A159469.
%K A176974 nonn,easy
%O A176974 3,3
%A A176974 _Thomas Quirk_, Apr 29 2010
%E A176974 Corrected and extended by _Ray Chandler_, Oct 16 2011