OFFSET
0,1
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).
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.
MATHEMATICA
Table[n^4 + 64, {n, 0, 40}]
PROG
(PARI) vector(40, n, n--; n^4+64)
(Sage) [n^4+64 for n in (0..40)]
(Maxima) makelist(n^4+64, n, 0, 40);
(Magma) [n^4+64: n in [0..40]];
(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
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Bruno Berselli, Apr 25 2016
STATUS
approved