OFFSET
0,1
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).
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.
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 *)
PROG
(PARI) vector(40, n, n--; n^4+324)
(Sage) [n^4+324 for n in (0..40)]
(Maxima) makelist(n^4+324, n, 0, 40);
(Magma) [n^4+324: n in [0..40]];
(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
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Bruno Berselli, Apr 25 2016
STATUS
approved