A212764 Number of (w,x,y,z) with all terms in {0,...,n}, w, x and y odd, and z odd.

0, 1, 8, 16, 54, 81, 192, 256, 500, 625, 1080, 1296, 2058, 2401, 3584, 4096, 5832, 6561, 9000, 10000, 13310, 14641, 19008, 20736, 26364, 28561, 35672, 38416, 47250, 50625, 61440, 65536, 78608, 83521, 99144, 104976, 123462, 130321

Offset: 0

Author

Clark Kimberling, May 29 2012

Keywords

• nonn
• easy

Comments

For a guide to related sequences, see A211795.

Links

• Index entries for linear recurrences with constant coefficients, signature (1,4,-4,-6,6,4,-4,-1,1).

Crossrefs

Cf. A211795.

Programs

Mathematica

t = Compile[{{n, _Integer}}, Module[{s = 0}, (Do[If[(Mod[w, 2] == 0) && (Mod[x, 2]== 0) && (Mod[y, 2] == 0) && (Mod[z, 2] == 1), s++], {w, 0, n}, {x, 0, n},
{y, 0, n}, {z, 0, n}]; s)]];
Map[t[#] &, Range[0, 40]]  (* A212764 *)
LinearRecurrence[{1, 4, -4, -6, 6, 4, -4, -1, 1}, {0, 1, 8, 16, 54, 81, 192, 256, 500}, 45]

Formula

a(n) = a(n-1) +4*a(n-2) -4*a(n-3) -6*a(n-4) +6*a(n-5) +4*a(n-6) -4*a(n-7) -a(n-8) +a(n-9).

G.f.: x*(1+7*x+4*x^2+10*x^3+x^4+x^5) / ( (1+x)^4*(1-x)^5 ).

a(n) = (2*n^4+10*n^3+18*n^2+12*n+1+(2*n^3+6*n^2+4*n-1)*(-1)^n)/32. - Luce ETIENNE, May 12 2015