OFFSET
0,2
COMMENTS
Every term is even.
For a guide to related sequences, see A211795.
LINKS
Index entries for linear recurrences with constant coefficients, signature (2,2,-6,0,6,-2,-2,1).
FORMULA
a(n) = 2*a(n-1)+2*a(n-2)-6*a(n-3)+6*a(n-5)-2*a(n-6)-2*a(n-7)+a(n-8).
G.f.: -2*x*(2+5*x+10*x^2+5*x^3+2*x^4) / ( (1+x)^3*(x-1)^5 ).
a(n) = (2n(n+2)-(-1)^n+1)(n+1)^2/8. [Bruno Berselli, Jun 11 2012]
MATHEMATICA
t = Compile[{{n, _Integer}}, Module[{s = 0}, (Do[If[(Mod[w, 2] == 0) && (Mod[x, 2] == 1), s++], {w, 0, n}, {x, 0, n}, {y, 0, n}, {z, 0, n}]; s)]];
Map[t[#] &, Range[0, 40]] (* A212766 *)
%/2 (* integers *)
LinearRecurrence[{2, 2, -6, 0, 6, -2, -2, 1}, {0, 4, 18, 64, 150, 324, 588, 1024}, 40]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, May 29 2012
STATUS
approved