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.

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

Links

Muniru A Asiru, Table of n, a(n) for n = 0..10000

Index entries for linear recurrences with constant coefficients, signature (2,2,-6,0,6,-2,-2,1).

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

Cf. A000982, A211795.

Sequence in context: A016790 A065733 A368245 * A302324 A303017 A281339

Adjacent sequences: A212890 A212891 A212892 * A212894 A212895 A212896

Keyword

nonn,easy

Author

Clark Kimberling, May 30 2012

Status

approved