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 A054556 a(n) = 4*n^2 - 9*n + 6. 36
 1, 4, 15, 34, 61, 96, 139, 190, 249, 316, 391, 474, 565, 664, 771, 886, 1009, 1140, 1279, 1426, 1581, 1744, 1915, 2094, 2281, 2476, 2679, 2890, 3109, 3336, 3571, 3814, 4065, 4324, 4591, 4866, 5149, 5440, 5739, 6046, 6361, 6684, 7015, 7354, 7701, 8056 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Move in 1-4 direction in a spiral organized like A068225 etc. Equals binomial transform of [1, 3, 8, 0, 0, 0, ...]. - Gary W. Adamson, Apr 30 2008 Ulam's spiral (N spoke). - Robert G. Wilson v, Oct 31 2011 Also, numbers of the form m*(4*m+1)+1 for nonpositive m. - Bruno Berselli, Jan 06 2016 LINKS Ivan Panchenko, Table of n, a(n) for n = 1..1000 Franck Ramaharo, Statistics on some classes of knot shadows, arXiv:1802.07701 [math.CO], 2018. Robert G. Wilson v, Cover of the March 1964 issue of Scientific American Index entries for linear recurrences with constant coefficients, signature (3,-3,1). FORMULA a(n)^2 = Sum_{i = 0..2*(4*n-5)} (4*n^2-13*n+9+i)^2*(-1)^i = ((n-1)*(4*n-5)+1)^2. - Bruno Berselli, Apr 29 2010 a(0)=1, a(1)=4, a(2)=15; for n > 2, a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Harvey P. Dale, Aug 21 2011 G.f.: -(6*x^2+x+1)/(x-1)^3. - Harvey P. Dale, Aug 21 2011 From Franck Maminirina Ramaharo, Mar 09 2018: (Start) a(n) = binomial(2*n - 2, 2) + 2*(n - 1)^2 + 1. a(n) = A000384(n-1) + A058331(n-1). a(n) = A130883(n-1) + A001105(n-1). (End) MAPLE a:=n->4*n^2-9*n+6: seq(a(n), n=0..50); # Muniru A Asiru, Mar 09 2018 MATHEMATICA a[n_] := 4*n^2 - 9*n + 6; Array[a, 40] (* Vladimir Joseph Stephan Orlovsky, Sep 01 2008 *) LinearRecurrence[{3, -3, 1}, {1, 4, 15}, 50] (* Harvey P. Dale, Sep 06 2015 *) CoefficientList[Series[-(6x^2 + x + 1)/(x - 1)^3, {x, 0, 49}], x] (* Robert G. Wilson v, Mar 12 2018 *) PROG (PARI) a(n)=4*n^2-9*n+6 \\ Charles R Greathouse IV, Sep 24 2015 (MAGMA) [4*n^2-9*n+6 : n in [1..50]]; // Vincenzo Librandi, Mar 10 2018 CROSSREFS Cf. A054555, A068225, A054552, A054554, A054567, A054569, A033951. Cf. A266883: m*(4*m+1)+1 for m = 0,-1,1,-2,2,-3,3,... Sequences on the four axes of the square spiral: Starting at 0: A001107, A033991, A007742, A033954; starting at 1: A054552, A054556, A054567, A033951. 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. 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. Sequence in context: A022265 A120389 A124150 * A113693 A211537 A213420 Adjacent sequences:  A054553 A054554 A054555 * A054557 A054558 A054559 KEYWORD nonn,easy AUTHOR Enoch Haga, G. L. Honaker, Jr., Apr 10 2000 EXTENSIONS Edited by Frank Ellermann, Feb 24 2002 Incorrect formula deleted by N. J. A. Sloane, Aug 02 2009 STATUS approved

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Last modified April 10 06:54 EDT 2021. Contains 342843 sequences. (Running on oeis4.)