A272298 a(n) = n^4 + 324.

324, 325, 340, 405, 580, 949, 1620, 2725, 4420, 6885, 10324, 14965, 21060, 28885, 38740, 50949, 65860, 83845, 105300, 130645, 160324, 194805, 234580, 280165, 332100, 390949, 457300, 531765, 614980, 707605, 810324, 923845, 1048900, 1186245, 1336660, 1500949, 1679940, 1874485, 2085460

Offset: 0

Author

Bruno Berselli, Apr 25 2016

Keywords

• nonn
• easy

Comments

This is the case k=3 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), A272297 (k=2).

Programs

Magma

[n^4+324: n in [0..40]];

Mathematica

Table[n^4 + 324, {n, 0, 40}]
LinearRecurrence[{5,-10,10,-5,1},{324,325,340,405,580},40] (* Harvey P. Dale, Jan 20 2021 *)

Maxima

makelist(n^4+324, n, 0, 40);

PARI

vector(40, n, n--; n^4+324)

Python

[n**4+324 for n in range(40)]

Python

for n in range(0, 10**5):print(n**4+324,end=", ") # Soumil Mandal, Apr 30 2016

Sage

[n^4+324 for n in (0..40)]

Formula

O.g.f.: (324 - 1295*x + 1955*x^2 - 1285*x^3 + 325*x^4)/(1 - x)^5. [Corrected by Georg Fischer, May 23 2019]

E.g.f.: (324 + x + 7*x^2 + 6*x^3 + x^4)*exp(x).

a(n) = (n^2 - 18)^2 + (6*n)^2.