OFFSET
0,2
COMMENTS
a(n) and its differences:
0, 2, 2, 3, 8, 10, 6, 7, 16,...
2, 0, 1, 5, 2, -4, 1, 9, 2,...
-2, 1, 4, -3, -6, 5, 8, -7, -10,... see A103889(n)
3, 3, -7, -3, 11, 3, -15, -3, 19,...
0, -10, 4, 14, -8, -18, 12, 22, -16,...
-10, 14, 10,- 22, -10, 30, 10, -38, -10,... .
The inverse binomial transform is
b(n)=0, 2, -2, 3, 0, -10, 24, -28, 0, 72, -160, 176, 0,...
=(0, 1, -1, 1, 0, -1, 4, -4, 0, 4, -16, 16, 0,...) * a(n).
LINKS
Index entries for linear recurrences with constant coefficients, signature (2,-3,4,-3,2,-1).
FORMULA
a(n) - a(n-4) = period 4:repeat 8, 8, 4, 4 = 4*A130658(n+2).
G.f.: (x^5 + 5*x^3 - 2*x^2 + 2*x)/((1-x)^2 * (1+x^2)^2). - Ralf Stephan, Jul 13 2013
MATHEMATICA
{2#[[1]], 2#[[2]], #[[3]], #[[4]]}&/@Partition[Range[0, 60], 4]//Flatten (* or *) LinearRecurrence[{2, -3, 4, -3, 2, -1}, {0, 2, 2, 3, 8, 10}, 60] (* Harvey P. Dale, Dec 14 2021 *)
CROSSREFS
KEYWORD
nonn,easy,changed
AUTHOR
Paul Curtz, Jul 09 2013
STATUS
approved