The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A190816 a(n) = 5*n^2 - 4*n + 1. 7
 1, 2, 13, 34, 65, 106, 157, 218, 289, 370, 461, 562, 673, 794, 925, 1066, 1217, 1378, 1549, 1730, 1921, 2122, 2333, 2554, 2785, 3026, 3277, 3538, 3809, 4090, 4381, 4682, 4993, 5314, 5645, 5986, 6337, 6698, 7069, 7450, 7841, 8242, 8653, 9074 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS For n >= 2, hypotenuses of primitive Pythagorean triangles with m = 2*n-1, where the sides of the triangle are a = m^2 - n^2, b = 2*n*m, c = m^2 + n^2; this sequence is the c values, short sides (a) are A045944(n-1), and long sides (b) are A002939(n). LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..2000 Index entries for linear recurrences with constant coefficients, signature (3,-3,1). FORMULA From Harvey P. Dale, May 24 2011: (Start) a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3); a(0)=1, a(1)=2, a(2)=13. G.f.: (1 - x + 10*x^2)/(1-x)^3. (End) E.g.f.: (1 + x + 5*x^2)*exp(x). - G. C. Greubel, Dec 03 2023 MATHEMATICA Table[5*n^2 - 4*n + 1, {n, 0, 100}] LinearRecurrence[{3, -3, 1}, {1, 2, 13}, 100] (* or *) CoefficientList[ Series[ (-10 x^2+x-1)/(x-1)^3, {x, 0, 100}], x] (* Harvey P. Dale, May 24 2011 *) PROG (Magma) [5*n^2 - 4*n + 1: n in [0..50]]; // Vincenzo Librandi, Jun 19 2011 (PARI) a(n)=5*n^2-4*n+1 \\ Charles R Greathouse IV, Oct 16 2015 (SageMath) [5*n^2-4*n+1 for n in range(41)] # G. C. Greubel, Dec 03 2023 CROSSREFS Short sides (a) A045944(n-1), long sides (b) A002939(n). Cf. A017281 (first differences), A051624 (a(n)-1), A202141. Sequences of the form m*n^2 - 4*n + 1: -A131098 (m=0), A028872 (m=1), A056220 (m=2), A045944 (m=3), A016754 (m=4), this sequence (m=5), A126587 (m=6), A339623 (m=7), A080856 (m=8). Sequence in context: A051474 A062708 A296293 * A084910 A124024 A102229 Adjacent sequences: A190813 A190814 A190815 * A190817 A190818 A190819 KEYWORD nonn,easy AUTHOR Vladimir Joseph Stephan Orlovsky, May 20 2011 EXTENSIONS Edited by Franklin T. Adams-Watters, May 20 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 | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified April 15 15:27 EDT 2024. Contains 371692 sequences. (Running on oeis4.)