OFFSET
0,3
COMMENTS
For a guide to related sequences, see A211795.
LINKS
Index entries for linear recurrences with constant coefficients, signature (1,3,-3,-3,3,1,-1).
FORMULA
a(n) = a(n-1)+3*a(n-2)-3*a(n-3)-3*a(n-4)+3*a(n-5)+a(n-6)-a(n-7).
G.f.: ( 1+4*x^2+2*x^3+x^4 ) / ( (1+x)^3*(1-x)^4 ).
a(n) = (4*n^3+15*n^2+20*n+12+3*(n^2+4*n+4)*(-1)^n)/24. - Luce ETIENNE, Jun 03 2014
MATHEMATICA
t = Compile[{{n, _Integer}}, Module[{s = 0}, (Do[If[(Mod[w, 2] == 0) && (Mod[x, 2] == 0 && w + x == y + z), s++], {w, 0, n}, {x, 0, n}, {y, 0, n}, {z, 0, n}]; s)]];
Map[t[#] &, Range[0, 50]] (* A212767 *)
LinearRecurrence[{1, 3, -3, -3, 3, 1, -1}, {1, 1, 8, 10, 29, 35, 72}, 50]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, May 29 2012
STATUS
approved