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A033951
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Write 1,2,... in clockwise spiral; sequence gives numbers on positive x axis.
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31
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1, 8, 23, 46, 77, 116, 163, 218, 281, 352, 431, 518, 613, 716, 827, 946, 1073, 1208, 1351, 1502, 1661, 1828, 2003, 2186, 2377, 2576, 2783, 2998, 3221, 3452, 3691, 3938, 4193, 4456, 4727, 5006, 5293, 5588, 5891, 6202, 6521, 6848, 7183, 7526, 7877, 8236
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Ulam's spiral (S spoke). - Robert G. Wilson v, Oct 31 2011
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LINKS
| Index entries for sequences related to linear recurrences with constant coefficients
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FORMULA
| a(n) = 4n^2+3n+1.
G.f.: (1+5x+2x^2)/(1-x)^3.
Equals A132774 * [1, 2, 3,...]; = binomial transform of [1, 7, 8, 0, 0, 0,...]. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Aug 28 2007
a(n) = a(n-1)+8*n-1 (with a(0)=1). [From Vincenzo Librandi, Nov 17 2010]
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EXAMPLE
| ... 16 5 6 7 22 ...
... 15 4 1 8 23 ...
... 14 3 2 9 24 ...
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MATHEMATICA
| lst={}; Do[p=4*n^2+3*n+1; AppendTo[lst, p], {n, 1, 6!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Sep 01 2008]
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PROG
| (PARI) a(n)=4*n^2+3*n+1
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CROSSREFS
| Sequences from spirals: A001107, A002939, A007742, A033951, A033952, A033953, A033954, A033989, A033990, A033991, A002943, A033996, A033988.
A014848(2n+1)=a(n).
Cf. A132774.
a(n) = A016754(n) - n. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), May 17 2009]
Sequence in context: A139433 A178072 A185257 * A175346 A027054 A048467
Adjacent sequences: A033948 A033949 A033950 * A033952 A033953 A033954
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KEYWORD
| nonn,easy,nice
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AUTHOR
| Olivier Gorin (gorin(AT)roazhon.inra.fr)
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EXTENSIONS
| Extended (with formula) by Erich Friedman (erich.friedman(AT)stetson.edu).
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