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A272297 a(n) = n^4 + 64.

%I A272297 #29 Sep 08 2022 08:46:16
%S A272297 64,65,80,145,320,689,1360,2465,4160,6625,10064,14705,20800,28625,
%T A272297 38480,50689,65600,83585,105040,130385,160064,194545,234320,279905,
%U A272297 331840,390689,457040,531505,614720,707345,810064,923585,1048640,1185985,1336400,1500689,1679680,1874225,2085200
%N A272297 a(n) = n^4 + 64.
%C A272297 This is the case k=2 of Sophie Germain's Identity n^4+(2*k^2)^2 = ((n-k)^2+k^2)*((n+k)^2+k^2).
%H A272297 Bruno Berselli, <a href="/A272297/b272297.txt">Table of n, a(n) for n = 0..1000</a>
%H A272297 Wikipedia, <a href="https://en.wikipedia.org/wiki/Sophie_Germain#Honors_in_number_theory">Sophie Germain's Identity</a>.
%H A272297 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F A272297 O.g.f.: (64 - 255*x + 395*x^2 - 245*x^3 + 65*x^4)/(1 - x)^5.
%F A272297 E.g.f.: (64 + x + 7*x^2 + 6*x^3 + x^4)*exp(x).
%F A272297 a(n) = (n^2 - 8)^2 + (4*n)^2.
%t A272297 Table[n^4 + 64, {n, 0, 40}]
%o A272297 (PARI) vector(40, n, n--; n^4+64)
%o A272297 (Sage) [n^4+64 for n in (0..40)]
%o A272297 (Maxima) makelist(n^4+64, n, 0, 40);
%o A272297 (Magma) [n^4+64: n in [0..40]];
%o A272297 (Python) [n**4+64 for n in range(40)]
%o A272297 (Python) for n in range(0,10**5):print(n**4+64) # _Soumil Mandal_, Apr 30 2016
%Y A272297 Cf. A005917.
%Y A272297 Subsequence of A227855.
%Y A272297 Cf. A000583 (k=0), A057781 (k=1), A272298 (k=3).
%K A272297 nonn,easy
%O A272297 0,1
%A A272297 _Bruno Berselli_, Apr 25 2016