OFFSET
0,2
COMMENTS
The terms of this sequence relate to intervals between cubes in the same fashion as terms of A002378 are related to intervals between squares.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
FORMULA
From R. J. Mathar, Nov 11 2008: (Start)
G.f.: x*(4+x+x^2)/(1-x)^4. (End)
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). - Vincenzo Librandi, May 06 2012
From A.H.M. Smeets, Sep 10 2018: (Start)
a(n) = Sum_{k=0..n-1} (n+1)^2-k for n >= 0 with empty domain of summation for n = 0.
a(n) = n*(n+1)^2 - n*(n-1)/2 for n >= 0.
Lim_{n -> inf} a(n-1)/n^3 = 1. (End)
E.g.f.: exp(x)*(8*x + 9*x^2 + 2*x^3)/2. - Stefano Spezia, Sep 12 2018
a(n) = A081435(n)-1. - R. J. Mathar, Sep 14 2018
MAPLE
seq(coeff(series(x*(x^2+x+4)/(1-x)^4, x, n+1), x, n), n = 0 .. 40); # Muniru A Asiru, Sep 11 2018
MATHEMATICA
Table[(n^3+(n+1)^3-1)/2, {n, 0, 70}] (* Vladimir Joseph Stephan Orlovsky, May 04 2011 *)
PROG
(PARI) j=[]; for (n=0, 40, j=concat(j, n^3+floor(((n+1)^3 - n^3)/2))); j
(PARI) a(n) = n*(2*n^2+3*n+3)/2; \\ Altug Alkan, Sep 20 2018
(Magma) I:=[0, 4, 17, 45]; [n le 4 select I[n] else 4*Self(n-1)-6*Self(n-2)+4*Self(n-3)-Self(n-4): n in [1..40]]; // Vincenzo Librandi, May 06 2012
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Alexander R. Povolotsky, Nov 09 2008
STATUS
approved