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A212762
Number of (w,x,y,z) with all terms in {0,...,n}, w and x odd, y even.
2
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.
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
KEYWORD
nonn
AUTHOR
Clark Kimberling, May 29 2012
STATUS
approved