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A212761
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Number of (w,x,y,z) with all terms in {0,...,n}, w odd, x and y even.
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2
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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
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OFFSET
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0,2
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COMMENTS
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Every term is even.
For a guide to related sequences, see A211795.
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LINKS
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Table of n, a(n) for n=0..36.
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FORMULA
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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).
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MATHEMATICA
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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]
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CROSSREFS
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Cf. A211795.
Sequence in context: A154252 A013198 A092345 * A102080 A000647 A133577
Adjacent sequences: A212758 A212759 A212760 * A212762 A212763 A212764
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KEYWORD
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nonn,easy
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AUTHOR
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Clark Kimberling, May 29 2012
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STATUS
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approved
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