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 A193068 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. 1
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Partial sums of A002939 starting at A002939(2). - R. J. Mathar, Aug 23 2011 LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..1000 Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1). FORMULA 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 a(n) = 4*a(n-1) -6*a(n-2) +4*a(n-3) -a(n-4). - Vincenzo Librandi, Jul 04 2012 EXAMPLE 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 MATHEMATICA CoefficientList[Series[(2*(6-3*x+x^2))/((x-1)^4), {x, 0, 50}], x] (* Vincenzo Librandi, Jul 04 2012 *) PROG (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 CROSSREFS Cf. A083374 (sum of areas for the first n triangles). Sequence in context: A005901 A090554 A009948 * A007586 A228391 A122973 Adjacent sequences:  A193065 A193066 A193067 * A193069 A193070 A193071 KEYWORD nonn,easy AUTHOR J. M. Bergot, Jul 15 2011 STATUS approved

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Last modified August 18 13:28 EDT 2018. Contains 313832 sequences. (Running on oeis4.)