

A054567


a(n) = 4*n^2  7*n + 4.


36



1, 6, 19, 40, 69, 106, 151, 204, 265, 334, 411, 496, 589, 690, 799, 916, 1041, 1174, 1315, 1464, 1621, 1786, 1959, 2140, 2329, 2526, 2731, 2944, 3165, 3394, 3631, 3876, 4129, 4390, 4659, 4936, 5221, 5514, 5815, 6124, 6441, 6766, 7099, 7440, 7789, 8146
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OFFSET

1,2


COMMENTS

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.
Ulam's spiral (W spoke of A054552).  Robert G. Wilson v, Oct 31 2011
Also, numbers of the form m*(4*m+1)+1 for nonnegative m. [Bruno Berselli, Jan 06 2016]


LINKS

Ivan Panchenko, Table of n, a(n) for n = 1..1000
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) = 8*n+a(n1)11 for n>1, a(1)=1.  Vincenzo Librandi, Aug 07 2010
a(n) = A204674(n1) / n. [Reinhard Zumkeller, Jan 18 2012]
a(n) = 3*a(n1)3*a(n2)+a(n3). G.f.: x*(4*x^2+3*x+1) / (x1)^3.  Colin Barker, Oct 25 2014


MATHEMATICA

Table[4 n^2  7 n + 4, {n, 100}] (* Vladimir Joseph Stephan Orlovsky, Sep 01 2008 *)


PROG

(PARI) Vec(x*(4*x^2+3*x+1)/(x1)^3 + O(x^100)) \\ Colin Barker, Oct 25 2014


CROSSREFS

Cf. A054566, A068225, A054552, A054554, A054556, 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: A090381 A106398 A179986 * A096957 A272811 A273206
Adjacent sequences: A054564 A054565 A054566 * A054568 A054569 A054570


KEYWORD

nonn,easy


AUTHOR

Enoch Haga, G. L. Honaker, Jr., Apr 10 2000


EXTENSIONS

Edited by Frank Ellermann, Feb 24 2002
Typo fixed by Charles R Greathouse IV, Oct 28 2009


STATUS

approved



