A212763 Number of (w,x,y,z) with all terms in {0,...,n}, and w, x and y odd.

0, 2, 3, 32, 40, 162, 189, 512, 576, 1250, 1375, 2592, 2808, 4802, 5145, 8192, 8704, 13122, 13851, 20000, 21000, 29282, 30613, 41472, 43200, 57122, 59319, 76832, 79576, 101250, 104625, 131072, 135168, 167042, 171955, 209952, 215784

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, A212759.

Programs

Mathematica

t = Compile[{{n, _Integer}}, Module[{s = 0}, (Do[If[(Mod[w, 2] == 1) && (Mod[x, 2] == 1) && (Mod[y, 2] == 1), s++], {w, 0, n}, {x, 0, n}, {y, 0, n}, {z, 0, n}]; s)]];
Map[t[#] &, Range[0, 50]]  (* A212763 *)
LinearRecurrence[{1, 4, -4, -6, 6, 4, -4, -1, 1}, {0, 2, 3, 32, 40,162, 189, 512, 576}, 45]

PARI

a(n) = (n+1)*(2*n^3+3*n^2+3*n+1-(3*n^2+3*n+1)*(-1)^n)/16;
vector(100, n, a(n-1)) \\ Altug Alkan, Oct 01 2015

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*(2+x+21*x^2+4*x^3+18*x^4+x^5+x^6) / ( (1+x)^4*(1-x)^5 ).

a(n) = (n+1)*(2*n^3+3*n^2+3*n+1-(3*n^2+3*n+1)*(-1)^n)/16. - Luce ETIENNE, Oct 01 2015

a(n) = A212759(-n-2). [Bruno Berselli, Oct 01 2015]