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0, 5, 18, 39, 68, 105, 150, 203, 264, 333, 410, 495, 588, 689, 798, 915, 1040, 1173, 1314, 1463, 1620, 1785, 1958, 2139, 2328, 2525, 2730, 2943, 3164, 3393, 3630, 3875, 4128, 4389, 4658, 4935, 5220, 5513, 5814, 6123, 6440, 6765, 7098, 7439, 7788, 8145
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Write 0,1,2,... in clockwise spiral; sequence gives numbers on positive y axis.
Central terms of the triangle in A126890. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Dec 30 2006
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REFERENCES
| S. M. Ellerstein, The square spiral, J. Recreational Mathematics 29 (#3, 1998) 188; 30 (#4, 1999-2000), 246-250.
R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics. Addison-Wesley, Reading, MA, 2nd ed., 1994, p. 99.
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Index to sequences with linear recurrences with constant coefficients, signature (3,-3,1).
Emilio Apricena, A version of the Ulam spiral
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FORMULA
| G.f.: x(5+3x)/(1-x)^3. - Michael Somos, Mar 03 2003
a(n) = floor((n + 1/4)^2). - Reinhard Zumkeller, Feb 20 2010
a(n) = A110654(n) + A173511(n) = A002943(n) - n. - Reinhard Zumkeller, Feb 20 2010
a(n) = 8n+a(n-1)-3. - Vincenzo Librandi, Nov 21 2010
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EXAMPLE
| Part of the spiral:
16 17 18 19 ...
15 4 5 6 ...
14 3 0 7 ...
13 2 1 8 ...
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MATHEMATICA
| s=0; lst={s}; Do[s+=n++ +5; AppendTo[lst, s], {n, 0, 7!, 8}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Nov 16 2008]
LinearRecurrence[{3, -3, 1}, {0, 5, 18}, 50] (* Vincenzo Librandi, Jan 29 2012 *)
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PROG
| (PARI) a(n)=4*n^2+n
(MAGMA) I:=[0, 5, 18]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..50]]; // Vincenzo Librandi, Jan 29 2012
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CROSSREFS
| a(n)=A033991(-n)=A074378(2n).
Sequences from spirals: A001107, A002939, A007742, A033951, A033952, A033953, A033954, A033989, A033990, A033991, A002943, A033996, A033988.
Cf. index to sequences with numbers of the form n*(d*n+10-d)/2 in A140090.
Sequence in context: A038346 A065007 A031428 * A000338 A056640 A160969
Adjacent sequences: A007739 A007740 A007741 * A007743 A007744 A007745
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KEYWORD
| nonn,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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