%I #29 Sep 08 2022 08:46:16

%S 64,65,80,145,320,689,1360,2465,4160,6625,10064,14705,20800,28625,

%T 38480,50689,65600,83585,105040,130385,160064,194545,234320,279905,

%U 331840,390689,457040,531505,614720,707345,810064,923585,1048640,1185985,1336400,1500689,1679680,1874225,2085200

%N a(n) = n^4 + 64.

%C 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 Bruno Berselli, <a href="/A272297/b272297.txt">Table of n, a(n) for n = 0..1000</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Sophie_Germain#Honors_in_number_theory">Sophie Germain's Identity</a>.

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).

%F O.g.f.: (64 - 255*x + 395*x^2 - 245*x^3 + 65*x^4)/(1 - x)^5.

%F E.g.f.: (64 + x + 7*x^2 + 6*x^3 + x^4)*exp(x).

%F a(n) = (n^2 - 8)^2 + (4*n)^2.

%t Table[n^4 + 64, {n, 0, 40}]

%o (PARI) vector(40, n, n--; n^4+64)

%o (Sage) [n^4+64 for n in (0..40)]

%o (Maxima) makelist(n^4+64, n, 0, 40);

%o (Magma) [n^4+64: n in [0..40]];

%o (Python) [n**4+64 for n in range(40)]

%o (Python) for n in range(0,10**5):print(n**4+64) # _Soumil Mandal_, Apr 30 2016

%Y Cf. A005917.

%Y Subsequence of A227855.

%Y Cf. A000583 (k=0), A057781 (k=1), A272298 (k=3).

%K nonn,easy

%O 0,1

%A _Bruno Berselli_, Apr 25 2016