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A054556
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4*n^2 - 9*n + 6.
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9
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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; internal format)
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OFFSET
| 1,2
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COMMENTS
| Move in 1-4 direction in a spiral organized like A068225 etc.
Ulam's spiral (N spoke). - Robert G. Wilson v, Oct 31 2011
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LINKS
| Index entries for sequences related to linear recurrences with constant coefficients, signature (3,-3,1).
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FORMULA
| Equals binomial transform of [1, 3, 8, 0, 0, 0,...] - Gary W. Adamson (qntmpkt(AT)yahoo.com), Apr 30 2008
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 [From Bruno Berselli (berselli.bruno(AT)yahoo.it), Apr 29 2010]
a(n)=8*n+a(n-1)-13 (with a(1)=1) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Aug 07 2010]
a(0)=1, a(1)=4, a(2)=15, a(n)=3*a(n-1)-3*a(n-2)+a(n-3) [From Harvey P. Dale, Aug 21 2011]
G.f.: -((6*x^2+x+1)/(x-1)^3) [From Harvey P. Dale, Aug 21 2011]
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MATHEMATICA
| f[n_] := 4*n^2 - 9*n + 6; Array[f, 40] [From Vladimir Orlovsky, Sep 01 2008]
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CROSSREFS
| Cf. A054555, A068225, A054552, A054554, A054567, A054569, A033951.
Sequence in context: A022265 A120389 A124150 * A113693 A190093 A077414
Adjacent sequences: A054553 A054554 A054555 * A054557 A054558 A054559
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KEYWORD
| easy,nonn
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AUTHOR
| Enoch Haga, G. L. Honaker, Jr. (Enokh(AT)comcast.net), Apr 10 2000
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EXTENSIONS
| Edited by Frank Ellermann, Feb 24 2002
Incorrect formula deleted by N. J. A. Sloane, Aug 02 2009
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