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A249547
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a(n) = (10*n^2+8*n-1+(-1)^n)/8.
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4
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0, 2, 7, 14, 24, 36, 51, 68, 88, 110, 135, 162, 192, 224, 259, 296, 336, 378, 423, 470, 520, 572, 627, 684, 744, 806, 871, 938, 1008, 1080, 1155, 1232, 1312, 1394, 1479, 1566, 1656, 1748, 1843, 1940, 2040, 2142, 2247, 2354, 2464, 2576, 2691, 2808, 2928, 3050
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OFFSET
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0,2
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COMMENTS
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a(n) is the number of lattice points (x,y) in the coordinate plane bounded by y < 3x, y >= x/2 and x <= n.
a(n)+1 is the number of lattice points bounded by y <= 3x, y >= x/2 and x <= n.
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LINKS
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FORMULA
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G.f.: x*(2+3*x)/((1-x)^3*(1+x)).
a(n) = 2*a(n-1)-2*a(n-3)+a(n-4) for n>3.
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MAPLE
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MATHEMATICA
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Table[(10*n^2 + 8 n - 1 + (-1)^n)/8 , {n, 0, 50}]
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PROG
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(Magma) [(10*n^2+8*n-1+(-1)^n)/8 : n in [0..50]];
(PARI) a(n) = (10*n^2+8*n-1+(-1)^n)/8; \\ Michel Marcus, Nov 04 2014
(PARI) concat(0, Vec(x*(2+3*x)/((1-x)^3*(1+x)) + O(x^100))) \\ Altug Alkan, Oct 28 2015
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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