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A054554 a(n) = 4n^2 - 10n + 7. 38
1, 3, 13, 31, 57, 91, 133, 183, 241, 307, 381, 463, 553, 651, 757, 871, 993, 1123, 1261, 1407, 1561, 1723, 1893, 2071, 2257, 2451, 2653, 2863, 3081, 3307, 3541, 3783, 4033, 4291, 4557, 4831, 5113, 5403, 5701, 6007, 6321, 6643, 6973, 7311, 7657, 8011, 8373 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Move in 1-3 direction in a spiral organized like A068225 etc.

Equals binomial transform of [1, 2, 8, 0, 0, 0, ...]. - Gary W. Adamson, May 03 2008

Ulam's spiral (NE spoke). - Robert G. Wilson v, Oct 31 2011

a(k+1) = 4k^2 - 2k + 1 in the Numberphile video. - Frank Ellermann, Mar 11 2020

LINKS

Ivan Panchenko, Table of n, a(n) for n = 1..1000

James Grime and Brady Haran, Prime Spirals, Numberphile video (2013).

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(n-1) - 14 with n > 1, a(1)=1. - Vincenzo Librandi, Aug 07 2010

G.f.: -x*(7*x^2+1)/(x-1)^3. - Colin Barker, Sep 21 2012

For n > 2, a(n) = A014105(n) + A014105(n-1). - Bruce J. Nicholson, May 07 2017

MAPLE

A054554:=n->4*n^2 -10*n + 7; seq(A054554(k), k=1..100); # Wesley Ivan Hurt, Nov 05 2013

MATHEMATICA

f[n_] := 4n^2 -10n + 7; Array[f, 40] (* Vladimir Joseph Stephan Orlovsky, Sep 01 2008 *)

PROG

(PARI) a(n)=4*n^2-10*n+7 \\ Charles R Greathouse IV, Nov 05 2013

CROSSREFS

Cf. A054553, A068225, A054552, A054556, A054567, A054569, A033951.

Cf. A014105.

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: A179026 A179027 A145907 * A051939 A257764 A146728

Adjacent sequences:  A054551 A054552 A054553 * A054555 A054556 A054557

KEYWORD

easy,nonn

AUTHOR

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

EXTENSIONS

Edited by Frank Ellermann, Feb 24 2002

STATUS

approved

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Last modified July 10 05:51 EDT 2020. Contains 335572 sequences. (Running on oeis4.)