OFFSET
0,3
COMMENTS
a(n)+a(n-1) is a perfect 6th power, hence a perfect square and a perfect cube.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (6,-14,14,0,-14,14,-6,1).
FORMULA
a(n) = (-1)^n + n*(3-5*n^2+3*n^4+n^5)/2. - R. J. Mathar, Mar 15 2011
a(n) = (-1)^n+A152725(n). - R. J. Mathar, Mar 15 2011
G.f. ( -1-78*x^2-267*x^3-337*x^4-36*x^5-8*x^6+x^7+6*x ) / ( (1+x)*(x-1)^7 ). - R. J. Mathar, Mar 15 2011
MATHEMATICA
CoefficientList[Series[(- 1 - 78 x^2 - 267 x^3 - 337 x^4 - 36 x^5 - 8 x^6 + x^7 + 6 x)/((1 + x) (x - 1)^7), {x, 0, 40}], x] (* Vincenzo Librandi, Oct 04 2013 *)
LinearRecurrence[{6, -14, 14, 0, -14, 14, -6, 1}, {1, 0, 64, 665, 3431, 12194, 34462, 83187}, 30] (* Harvey P. Dale, Apr 30 2020 *)
PROG
(Magma) [(-1)^n + n*(3-5*n^2+3*n^4+n^5)/2: n in [0..30]]; // Vincenzo Librandi, Oct 04 2013
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Mar 12 2011
STATUS
approved