OFFSET
0,1
REFERENCES
Donald E. Knuth, The Art of Computer Programming, Addison-Wesley, Reading, MA, 1997, Vol. 1, exercise 1.2.1, Nr. 11, p. 19. [From Reinhard Zumkeller, Apr 11 2010]
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
FORMULA
G.f.: -(5*x^4-5*x^3+35*x^2-15*x+4) / (x-1)^5. - Colin Barker, Mar 29 2013
a(n) = A002523(n) + 3.
Sum_{k=0..n} A033999(k)*A016755(k)/a(k) = A033999(n)*(n+1)/A053755(n+1), see Knuth reference. - Reinhard Zumkeller, Apr 11 2010
a(n) = (n^2)^2 + 2^2 = (n^2-2)^2 + (2*n)^2. - Thomas Ordowski, Sep 15 2015
a(n) = A272298(3*n)/3^4. - Bruno Berselli, Apr 29 2016
Sum_{n>=0} 1/a(n) = (Pi*coth(Pi) + 1)/8. - Amiram Eldar, Oct 04 2021
MATHEMATICA
Table[n^4+4, {n, 0, 60}] (* Vladimir Joseph Stephan Orlovsky, Apr 15 2011 *)
LinearRecurrence[{5, -10, 10, -5, 1}, {4, 5, 20, 85, 260}, 40] (* Harvey P. Dale, Aug 20 2020 *)
PROG
(Magma) [n^4+4: n in [0..40]]; // Vincenzo Librandi, Sep 07 2011
(PARI) first(m)=vector(m, i, i--; i^4+4) \\ Anders Hellström, Sep 15 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Henry Bottomley, Nov 04 2000
STATUS
approved