login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A054556 a(n) = 4*n^2 - 9*n + 6. 14
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

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(n) = 8*n+a(n-1)-13 for n>1, a(1)=1. - Vincenzo Librandi, Aug 07 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

MATHEMATICA

f[n_] := 4*n^2 - 9*n + 6; Array[f, 40] (* Vladimir Joseph Stephan Orlovsky, Sep 01 2008 *)

LinearRecurrence[{3, -3, 1}, {1, 4, 15}, 50] (* Harvey P. Dale, Sep 06 2015 *)

PROG

(PARI) a(n)=4*n^2-9*n+6 \\ Charles R Greathouse IV, Sep 24 2015

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,...

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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified June 25 06:13 EDT 2017. Contains 288709 sequences.