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A193068
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Generating primitive Pythagorean triangles by using (n, n+1) gives perimeters for each n. This sequence list the sum of these perimeters for each n triangles.
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1
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12, 42, 98, 188, 320, 502, 742, 1048, 1428, 1890, 2442, 3092, 3848, 4718, 5710, 6832, 8092, 9498, 11058, 12780, 14672, 16742, 18998, 21448, 24100, 26962, 30042, 33348, 36888, 40670, 44702, 48992, 53548, 58378, 63490, 68892, 74592, 80598, 86918, 93560
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OFFSET
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1,1
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COMMENTS
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Partial sums of A002939 starting at A002939(2). - R. J. Mathar, Aug 23 2011
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LINKS
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FORMULA
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a(n) = n*(4*n^2 + 15*n + 17)/3.
G.f. ( 2*x*(6-3*x+x^2) ) / ( (x-1)^4 ). - R. J. Mathar, Aug 23 2011
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EXAMPLE
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The perimeters of the first five triangles produced
by pairs (1,2), (2,3), (3,4), 4,5) (5,6) are in order
12, 30, 56, 90, 132 with sum 320. From the formula
(4*5^3 + 15*5^2 + 17*5)/3 = 320
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MATHEMATICA
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CoefficientList[Series[(2*(6-3*x+x^2))/((x-1)^4), {x, 0, 50}], x] (* Vincenzo Librandi, Jul 04 2012 *)
LinearRecurrence[{4, -6, 4, -1}, {12, 42, 98, 188}, 40] (* Harvey P. Dale, Oct 29 2022 *)
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PROG
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(Magma) I:=[12, 42, 98, 188]; [n le 4 select I[n] else 4*Self(n-1)-6*Self(n-2)+4*Self(n-3)-Self(n-4): n in [1..40]]; // Vincenzo Librandi, Jul 04 2012
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CROSSREFS
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Cf. A083374 (sum of areas for the first n triangles).
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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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