A212762 Number of (w,x,y,z) with all terms in {0,...,n}, w and x odd, y even.

0, 2, 6, 32, 60, 162, 252, 512, 720, 1250, 1650, 2592, 3276, 4802, 5880, 8192, 9792, 13122, 15390, 20000, 23100, 29282, 33396, 41472, 46800, 57122, 63882, 76832, 85260, 101250, 111600, 131072, 143616, 167042, 182070, 209952, 227772

Offset

0,2

Comments

Every term is even.

For a guide to related sequences, see A211795.

Links

Table of n, a(n) for n=0..36.

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

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.: 2*x*(1+2*x+9*x^2+6*x^3+5*x^4+x^5) / ( (1+x)^4*(1-x)^5 ).

a(n) = (n+1)*(2*n^3+5*n^2+3*n+1-(n^2+3*n+1)*(-1)^n)/16. - Luce ETIENNE, Sep 19 2015

Mathematica

t = Compile[{{n, _Integer}},  Module[{s = 0}, (Do[If[(Mod[w, 2] == 1) && (Mod[x, 2] == 1) && (Mod[y, 2] == 0), s++], {w, 0, n}, {x, 0, n}, {y, 0, n}, {z, 0, n}]; s)]];
Map[t[#] &, Range[0, 50]]  (* A212762 *)
%/2 (* integers *)
LinearRecurrence[{1, 4, -4, -6, 6, 4, -4, -1, 1}, {0, 2, 6, 32, 60, 162, 252, 512, 720}, 45]

Crossrefs

Cf. A211795.

Sequence in context: A340232 A109243 A223586 * A108327 A188573 A196010

Adjacent sequences: A212759 A212760 A212761 * A212763 A212764 A212765

Keyword

nonn

Author

Clark Kimberling, May 29 2012

Status

approved