OFFSET
0,2
COMMENTS
For a guide to related sequences, see A211422.
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (2,-1,0,2,-4,2,0,-1,2,-1).
FORMULA
a(n) = 2*a(n-1) - a(n-2) + 2*a(n-4) - 4*a(n-5) + 2*a(n-6) - a(n-8) + 2*a(n-9) - a(n-10) for n>9.
G.f.: x*(4 + 24*x + 48*x^2 + 66*x^3 + 92*x^4 + 72*x^5 + 48*x^6 + 23*x^7 + 7*x^8) / ((1 - x)^4*(1 + x)^2*(1 + x^2)^2). - Colin Barker, Dec 05 2017
MATHEMATICA
t = Compile[{{u, _Integer}},
Module[{s = 0}, (Do[If[w + 4 x + 4 y > 0,
s = s + 1], {w, #}, {x, #}, {y, #}] &[
Flatten[{Reverse[-#], #} &[Range[1, u]]]]; s)]];
Map[t[#] &, Range[0, 60]] (* A211626 *)
FindLinearRecurrence[%]
(* Peter J. C. Moses, Apr 13 2012 *)
LinearRecurrence[{2, -1, 0, 2, -4, 2, 0, -1, 2, -1}, {0, 4, 32, 108, 250, 492, 854, 1360, 2021, 2885}, 40] (* Harvey P. Dale, Nov 29 2013 *)
PROG
(PARI) concat(0, Vec(x*(4 + 24*x + 48*x^2 + 66*x^3 + 92*x^4 + 72*x^5 + 48*x^6 + 23*x^7 + 7*x^8) / ((1 - x)^4*(1 + x)^2*(1 + x^2)^2) + O(x^40))) \\ Colin Barker, Dec 05 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Apr 17 2012
STATUS
approved