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 A212761 Number of (w,x,y,z) with all terms in {0,...,n}, w odd, x and y even. 2
 0, 2, 12, 32, 90, 162, 336, 512, 900, 1250, 1980, 2592, 3822, 4802, 6720, 8192, 11016, 13122, 17100, 20000, 25410, 29282, 36432, 41472, 50700, 57122, 68796, 76832, 91350, 101250, 119040, 131072, 152592, 167042, 192780, 209952, 240426 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Every term is even. For a guide to related sequences, see A211795. LINKS 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 + 10*x^2 + 12*x^3 + 18*x^4 + 4*x^5 + 2*x^6)/(1 - x - 4*x^2 + 4*x^3 + 6*x^4 - 6*x^5 - 4*x^6 + 4*x^7 + x^8 - x^9). MATHEMATICA t = Compile[{{n, _Integer}}, Module[{s = 0}, (Do[If[(Mod[w, 2] == 1) && (Mod[x, 2] == 0) && (Mod[y, 2] == 0), s++], {w, 0, n}, {x, 0, n}, {y, 0, n}, {z, 0, n}]; s)]]; Map[t[#] &, Range[0, 50]]  (* A212761 *) %/2 (* integers *) LinearRecurrence[{1, 4, -4, -6, 6, 4, -4, -1, 1}, {0, 2, 12, 32, 90, 162, 336, 512, 900}, 45] CROSSREFS Cf. A211795. Sequence in context: A154252 A013198 A092345 * A102080 A000647 A133577 Adjacent sequences:  A212758 A212759 A212760 * A212762 A212763 A212764 KEYWORD nonn,easy AUTHOR Clark Kimberling, May 29 2012 STATUS approved

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