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A279169
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a(n) = floor( 4*n^2/5 ).
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3
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0, 0, 3, 7, 12, 20, 28, 39, 51, 64, 80, 96, 115, 135, 156, 180, 204, 231, 259, 288, 320, 352, 387, 423, 460, 500, 540, 583, 627, 672, 720, 768, 819, 871, 924, 980, 1036, 1095, 1155, 1216, 1280, 1344, 1411, 1479, 1548, 1620, 1692, 1767, 1843, 1920, 2000, 2080, 2163, 2247
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OFFSET
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0,3
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LINKS
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FORMULA
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O.g.f.: x^2*(3 + x + x^2 + 3*x^3)/((1 - x)^3*(1 + x + x^2 + x^3 + x^4)).
a(n) = a(-n) = 2*a(n-1) - a(n-2) + a(n-5) - 2*a(n-6) + a(n-7).
a(5*m+r) = 4*m*(5*m + 2*r) + a(r), where m >= 0 and 0 <= r < 5. Example: for m=4 and r=3, a(5*4+3) = a(23) = 4*4*(5*4 + 2*3) + a(3) = 416 + 7 = 423.
Sum_{n>=2} 1/a(n) = Pi^2/120 + sqrt(29 - 62/sqrt(5))*Pi/8 + 5/16. - Amiram Eldar, Sep 26 2022
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MATHEMATICA
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Table[Floor[4 n^2/5], {n, 0, 60}]
LinearRecurrence[{2, -1, 0, 0, 1, -2, 1}, {0, 0, 3, 7, 12, 20, 28}, 60] (* Harvey P. Dale, Nov 07 2020 *)
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PROG
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(PARI) vector(60, n, n--; floor(4*n^2/5))
(Python) [int(4*n**2/5) for n in range(60)]
(Sage) [floor(4*n^2/5) for n in range(60)]
(Magma) [4*n^2 div 5: n in [0..60]];
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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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