The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Please make a donation to keep the OEIS running. We are now in our 56th year. In the past year we added 10000 new sequences and reached almost 9000 citations (which often say "discovered thanks to the OEIS"). Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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 A334277 Adjacent sequences:  A193065 A193066 A193067 * A193069 A193070 A193071 KEYWORD nonn,easy AUTHOR J. M. Bergot, Jul 15 2011 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 2 16:34 EST 2020. Contains 338877 sequences. (Running on oeis4.)