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

64, 65, 80, 145, 320, 689, 1360, 2465, 4160, 6625, 10064, 14705, 20800, 28625, 38480, 50689, 65600, 83585, 105040, 130385, 160064, 194545, 234320, 279905, 331840, 390689, 457040, 531505, 614720, 707345, 810064, 923585, 1048640, 1185985, 1336400, 1500689, 1679680, 1874225, 2085200

Offset: 0

Author

Bruno Berselli, Apr 25 2016

Keywords

• nonn
• easy

Comments

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).

Links

• Bruno Berselli, Table of n, a(n) for n = 0..1000
• Wikipedia, Sophie Germain's Identity.
• Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Crossrefs

Cf. A005917.

Subsequence of A227855.

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

Programs

Magma

[n^4+64: n in [0..40]];

Mathematica

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

Maxima

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

PARI

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

Python

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

Python

for n in range(0,10**5):print(n**4+64) # Soumil Mandal, Apr 30 2016

Sage

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

Formula

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

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

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