OFFSET
0,3
COMMENTS
For a guide to related sequences, see A211795.
LINKS
Index entries for linear recurrences with constant coefficients, signature (2, -1, 2, -4, 2, -1, 2, -1).
FORMULA
a(n) = 2*a(n-1)-a(n-2)+2*a(n-3)-4*a(n-4)+2*a(n-5)-a(n-6)+2*a(n-7)-a(n-8).
G.f.: (x + 2*x^2 + 10*x^3 + 14*x^4 + 10*x^5 + 2*x^6 + x^7)/(1 - 2*x + x^2 - 2*x^3 + 4*x^4 - 2*x^5 + x^6 - 2*x^7 + x^8). [corrected by Georg Fischer, May 03 2019]
MATHEMATICA
t = Compile[{{n, _Integer}}, Module[{s = 0},
(Do[If[Abs[w - x] == 2 Abs[x - y] - Abs[y - z],
s = s + 1],
{w, 1, #}, {x, 1, #}, {y, 1, #}, {z, 1, #}] &[n]; s)]];
Map[t[#] &, Range[0, 40]] (* A212577 *)
LinearRecurrence[{2, -1, 2, -4, 2, -1, 2, -1}, {0, 1, 4, 17, 46, 89, 154, 251}, 45]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, May 22 2012
STATUS
approved