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A045947
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Triangles in open triangular matchstick arrangement (triangle minus one side) of side n.
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10
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0, 0, 2, 7, 17, 33, 57, 90, 134, 190, 260, 345, 447, 567, 707, 868, 1052, 1260, 1494, 1755, 2045, 2365, 2717, 3102, 3522, 3978, 4472, 5005, 5579, 6195, 6855, 7560, 8312, 9112, 9962, 10863, 11817, 12825, 13889, 15010, 16190, 17430, 18732, 20097, 21527
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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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a(n) = (1/16)*(2*n*(2*n^2+n-2)+(-1)^n-1). - Bruno Berselli, Aug 29 2011
E.g.f.: (x*(1 + 7*x + 2*x^2)*cosh(x) - (1 - x - 7*x^2 - 2*x^3)*sinh(x))/8. - Stefano Spezia, Aug 22 2023
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MATHEMATICA
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LinearRecurrence[{3, -2, -2, 3, -1}, {0, 0, 2, 7, 17}, 45] (* Jean-François Alcover, Dec 12 2016 *)
CoefficientList[Series[(2x^2+x^3)/((1-x)^3(1-x^2)), {x, 0, 50}], x] (* Harvey P. Dale, Jun 26 2021 *)
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PROG
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(PARI) a(n)=(4*n^3+2*n^2-4*n)\16
(Magma) [Floor((4*n^3+2*n^2-4*n)/16): n in [0..50]]; // Vincenzo Librandi, Aug 29 2011
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CROSSREFS
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KEYWORD
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nonn,easy,nice
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AUTHOR
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STATUS
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approved
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