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A212893
Number of quadruples (w,x,y,z) with all terms in {0,...,n} such that w-x, x-y, and y-z all have the same parity.
2
1, 4, 25, 64, 169, 324, 625, 1024, 1681, 2500, 3721, 5184, 7225, 9604, 12769, 16384, 21025, 26244, 32761, 40000, 48841, 58564, 70225, 82944, 97969, 114244, 133225, 153664, 177241, 202500, 231361, 262144, 297025, 334084, 375769
OFFSET
0,2
COMMENTS
For a guide to related sequences, see A211795.
Sum of odd integers between 1 and (n+1)^2. - Réjean Labrie, Jan 14 2014
FORMULA
a(n) = (A000982(n+1))^2.
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.: f(x)/g(x), where f(x) = -1 - 2*x - 15*x^2 - 12*x^3 - 15*x^4 - 2*x^5 - x^6 and g(x) = ((-1+x)^5)*(1+x)^3.
MAPLE
A212893 := n->ceil((n+1)^2/2)^2; seq(A212893(k), k=1..100); # Wesley Ivan Hurt, Jun 14 2013
MATHEMATICA
t = Compile[{{n, _Integer}}, Module[{s = 0},
(Do[If[Mod[w - x, 2] == Mod[x - y, 2] == Mod[y - z, 2], s = s + 1],
{w, 0, n}, {x, 0, n}, {y, 0, n}, {z, 0, n}]; s)]];
m = Map[t[#] &, Range[0, 40]] (* this sequence *)
Sqrt[m] (* A000982 except for offset *)
CROSSREFS
Sequence in context: A016790 A065733 A368245 * A376483 A302324 A303017
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, May 30 2012
STATUS
approved