# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a054567 Showing 1-1 of 1 %I A054567 #65 Aug 03 2024 19:23:04 %S A054567 1,6,19,40,69,106,151,204,265,334,411,496,589,690,799,916,1041,1174, %T A054567 1315,1464,1621,1786,1959,2140,2329,2526,2731,2944,3165,3394,3631, %U A054567 3876,4129,4390,4659,4936,5221,5514,5815,6124,6441,6766,7099,7440,7789,8146,8511,8884 %N A054567 a(n) = 4*n^2 - 7*n + 4. %C A054567 The number 1 is placed in the middle of a sheet of squared paper and the numbers 2, 3, 4, 5, 6, etc. are written in a clockwise spiral around 1, as in A068225 etc. This sequence is read off along one of the rays from 1. %C A054567 Ulam's spiral (W spoke of A054552). - _Robert G. Wilson v_, Oct 31 2011 %C A054567 Also, numbers of the form m*(4*m+1)+1 for nonnegative m. - _Bruno Berselli_, Jan 06 2016 %C A054567 The sequence forms the 1x2 diagonal of the square maze arrangement in A081344. - _Jarrod G. Sage_, Jul 17 2024 %H A054567 Ivan Panchenko, Table of n, a(n) for n = 1..1000 %H A054567 Robert G. Wilson v, Cover of the March 1964 issue of Scientific American %H A054567 Index entries for linear recurrences with constant coefficients, signature (3,-3,1). %F A054567 a(n) = 8*n+a(n-1)-11 for n>1, a(1)=1. - _Vincenzo Librandi_, Aug 07 2010 %F A054567 a(n) = A204674(n-1) / n. - _Reinhard Zumkeller_, Jan 18 2012 %F A054567 From _Colin Barker_, Oct 25 2014: (Start) %F A054567 a(n) = 3*a(n-1)-3*a(n-2)+a(n-3). %F A054567 G.f.: -x*(4*x^2+3*x+1) / (x-1)^3. (End) %F A054567 E.g.f.: exp(x)*(4 - 3*x + 4*x^2) - 4. - _Stefano Spezia_, Apr 24 2024 %F A054567 a(n) = A016742(n-1) + n. - _Jarrod G. Sage_, Jul 17 2024 %t A054567 Table[4 n^2 - 7 n + 4, {n, 100}] (* _Vladimir Joseph Stephan Orlovsky_, Sep 01 2008 *) %o A054567 (PARI) Vec(-x*(4*x^2+3*x+1)/(x-1)^3 + O(x^100)) \\ _Colin Barker_, Oct 25 2014 %Y A054567 Cf. A054566, A068225, A054552, A054554, A054556, A054569, A033951, A204674. %Y A054567 Cf. A266883: m*(4*m+1)+1 for m = 0,-1,1,-2,2,-3,3,... %Y A054567 Sequences on the four axes of the square spiral: Starting at 0: A001107, A033991, A007742, A033954; starting at 1: A054552, A054556, A054567, A033951. %Y A054567 Sequences on the four diagonals of the square spiral: Starting at 0: A002939 = 2*A000384, A016742 = 4*A000290, A002943 = 2*A014105, A033996 = 8*A000217; starting at 1: A054554, A053755, A054569, A016754. %Y A054567 Sequences obtained by reading alternate terms on the X and Y axes and the two main diagonals of the square spiral: Starting at 0: A035608, A156859, A002378 = 2*A000217, A137932 = 4*A002620; starting at 1: A317186, A267682, A002061, A080335. %K A054567 nonn,easy %O A054567 1,2 %A A054567 _Enoch Haga_, _G. L. Honaker, Jr._, Apr 10 2000 %E A054567 Edited by _Frank Ellermann_, Feb 24 2002 %E A054567 Typo fixed by _Charles R Greathouse IV_, Oct 28 2009 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE