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A308096
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Take all the integer-sided triangles with perimeter n and sides a, b, and c such that a <= b <= c. a(n) is the sum of all the b's.
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1
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0, 0, 1, 0, 2, 2, 5, 3, 10, 7, 16, 13, 24, 20, 38, 29, 50, 45, 69, 58, 92, 79, 117, 104, 146, 131, 186, 162, 222, 205, 270, 243, 324, 294, 381, 351, 444, 411, 523, 477, 596, 560, 686, 636, 784, 730, 886, 832, 996, 938, 1127, 1052, 1250, 1188, 1395, 1315
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OFFSET
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1,5
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LINKS
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FORMULA
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a(n) = Sum_{k=1..floor(n/3)} Sum_{i=k..floor((n-k)/2)} sign(floor((i+k)/(n-i-k+1))) * i.
G.f.: x^3*(1 + x + 2*x^2 + 2*x^3 + 3*x^4 + 2*x^5 + 2*x^6) / ((1 - x)^4*(1 + x)^3*(1 + x^2)^2*(1 + x + x^2)^2).
a(n) = -a(n-1) + 2*a(n-3) + 4*a(n-4) + 2*a(n-5) - a(n-6) - 5*a(n-7) - 5*a(n-8) - a(n-9) + 2*a(n-10) + 4*a(n-11) + 2*a(n-12) - a(n-14) - a(n-15) for n>15.
(End)
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MATHEMATICA
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Table[Sum[Sum[i*Sign[Floor[(i + k)/(n - i - k + 1)]], {i, k, Floor[(n - k)/2]}], {k, Floor[n/3]}], {n, 100}]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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