OFFSET
0,3
COMMENTS
First trisection of A011865.
LINKS
Bruno Berselli, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,-4,4,-3,1).
FORMULA
G.f.: x^2*(2 + x^2)/((1 + x^2)*(1 - x)^3).
a(n) = ( n*(3*n-1) + i^(n*(n+1)) - 1 )/4, where i=sqrt(-1).
MATHEMATICA
Table[Floor[n (3 n - 1)/4], {n, 0, 60}]
CoefficientList[Series[x^2(2+x^2)/((1+x^2)(1-x)^3), {x, 0, 70}], x] (* or *) LinearRecurrence[{3, -4, 4, -3, 1}, {0, 0, 2, 6, 11}, 70] (* Harvey P. Dale, Jan 28 2022 *)
PROG
(Magma) [Floor(n*(3*n-1)/4): n in [0..60]];
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Bruno Berselli, Nov 11 2013
STATUS
approved