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A330520
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Sum of even integers <= n times the sum of odd integers <= n.
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1
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0, 0, 2, 8, 24, 54, 108, 192, 320, 500, 750, 1080, 1512, 2058, 2744, 3584, 4608, 5832, 7290, 9000, 11000, 13310, 15972, 19008, 22464, 26364, 30758, 35672, 41160, 47250, 54000, 61440, 69632, 78608, 88434, 99144, 110808, 123462, 137180, 152000, 168000, 185220, 203742, 223608, 244904, 267674
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OFFSET
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0,3
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COMMENTS
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Number of crossings in a grid formed by drawing n parallel infinite-length lines perpendicular to the previous number of lines.
The sum of odd integers <= n is m^2 where m = round(n/2) is their number. The sum of even integers <= n is k(k+1) where k = floor(n/2) is their number. So a(n) = m^2*k(k+1), where the factor m appears three times. - M. F. Hasler, Dec 19 2019
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LINKS
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FORMULA
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G.f.: 2*(x^2+x+1)*x^2/((x+1)^2*(1-x)^5).
a(2k+i) = (k+i)^3 (k+1-i), with i = 0 or 1. - M. F. Hasler, Dec 19 2019
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MATHEMATICA
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CoefficientList[Series[2 (x^2 + x + 1) x^2/((x + 1)^2*(1 - x)^5), {x, 0, 45}], x] (* Michael De Vlieger, Dec 22 2019 *)
LinearRecurrence[{3, -1, -5, 5, 1, -3, 1}, {0, 0, 2, 8, 24, 54, 108}, 50] (* Harvey P. Dale, Dec 29 2021 *)
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PROG
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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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