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A242477
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a(n) = floor(3*n^2/4).
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3
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0, 0, 3, 6, 12, 18, 27, 36, 48, 60, 75, 90, 108, 126, 147, 168, 192, 216, 243, 270, 300, 330, 363, 396, 432, 468, 507, 546, 588, 630, 675, 720, 768, 816, 867, 918, 972, 1026, 1083, 1140, 1200, 1260, 1323, 1386, 1452, 1518, 1587, 1656, 1728, 1800, 1875
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OFFSET
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0,3
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COMMENTS
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The even-numbered terms are the same as the three - quarter squares; the odd-numbered terms are one less.
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LINKS
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FORMULA
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a(n) = a(n-2) + 3*(n-1) for n>1, a(0) = a(1) = 0.
G.f.: 3*x^2/((1-x)^2*(1-x^2)).
Sum_{n>=2} 1/a(n) = Pi^2/18 + 1/3. - Amiram Eldar, Feb 16 2023
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MATHEMATICA
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Table[Floor[3 n^2/4], {n, 0, 60}]
LinearRecurrence[{2, 0, -2, 1}, {0, 0, 3, 6}, 60] (* Harvey P. Dale, Sep 07 2019 *)
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PROG
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(Magma) [Floor(3*n^2/4): n in [0..60]];
(Sage) [3*floor(n^2/4) for n in (0..60)] # Bruno Berselli, May 22 2014
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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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