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

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A168235 1+5*n+7*n^2. 4
 13, 39, 79, 133, 201, 283, 379, 489, 613, 751, 903, 1069, 1249, 1443, 1651, 1873, 2109, 2359, 2623, 2901, 3193, 3499, 3819, 4153, 4501, 4863, 5239, 5629, 6033, 6451, 6883, 7329, 7789, 8263, 8751, 9253, 9769, 10299, 10843, 11401, 11973, 12559, 13159, 13773 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Consider the quadratic cyclotomic polynomial f(x) = x^2+x+1 and the quotients defined by f(x + n*f(x))/f(x). a(n) is the quotient at x=2. See A168240 for x=3 or A168244 for x= 1+sqrt(-5). LINKS Harvey P. Dale, Table of n, a(n) for n = 1..1000 Index entries for linear recurrences with constant coefficients, signature (3,-3,1). FORMULA a(1)=13, a(2)=39, a(3)=79, a(n)=3*a(n-1)-3*a(n-2)+a(n-3). - Harvey P. Dale, Feb 07 2015 From G. C. Greubel, Apr 09 2016: (Start) G.f.: (1 + 10*x + 3*x^2)/(1-x)^3. E.g.f.: (1 + 12*x + 7*x^2)*exp(x). (End) EXAMPLE When x = 2, f(x) = 7. Hence at n=1, f( x + f(x))/f(x) = 13 = a(1). MATHEMATICA Table[1+5n+7n^2, {n, 60}] (* or *) LinearRecurrence[{3, -3, 1}, {13, 39, 79}, 60] (* Harvey P. Dale, Feb 07 2015 *) PROG (PARI) a(n)=1+5*n+7*n^2 \\ Charles R Greathouse IV, Jun 17 2017 CROSSREFS Cf. A165806, A165808, A165809. Sequence in context: A158647 A283123 A152741 * A258597 A299816 A041324 Adjacent sequences: A168232 A168233 A168234 * A168236 A168237 A168238 KEYWORD nonn,easy AUTHOR A.K. Devaraj, Nov 21 2009 EXTENSIONS Edited, definition simplified, sequence extended beyond a(8) by R. J. Mathar, Nov 23 2009 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 December 10 01:29 EST 2022. Contains 358711 sequences. (Running on oeis4.)