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Search: id:A002943
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| 0, 6, 20, 42, 72, 110, 156, 210, 272, 342, 420, 506, 600, 702, 812, 930, 1056, 1190, 1332, 1482, 1640, 1806, 1980, 2162, 2352, 2550, 2756, 2970, 3192, 3422, 3660, 3906, 4160, 4422, 4692, 4970, 5256, 5550
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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a(n) = number of edges in (n+1)X(n+1) square grid with all horizontal, vertical and diagonal segments filled in - Asher Auel (asher.auel(AT)reed.edu) Jan 12, 2000.
Write 0,1,2,... in clockwise spiral; sequence gives numbers on one of 4 diagonals.
Twice second hexagonal numbers (Cf. A014105). - Omar E. Pol (info(AT)polprimos.com), May 21 2008
If A=[A002943] 4*n.^2+2*n (n>0, 6,20,42,. ,.,); Y=[A007395] 2 (2, 2, 2,..,); X=[A016813] 4*n+1 (n>0, 5,9,13,17, ,. .,), we have, for all terms, Pell's equation X^2-A*Y^2=1. Example: 5^2-6 *2^2=1; 9^2-20*2^2=1; 13^2-42*2^2=1. [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 11 2009]
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REFERENCES
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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
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T. D. Noe, Table of n, a(n) for n=0..1000
Eric Weisstein's World of Mathematics, Queen's Tour Graph
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FORMULA
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4n^2+2n.
a(n)=A014105(n)*2. - Omar E. Pol (info(AT)polprimos.com), May 21 2008
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EXAMPLE
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16 17 18 19 ...
15 4 5 6 ...
14 3 0 7 ...
13 2 1 8 ...
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MAPLE
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a:=n->sum(n+1, j=1..n): seq(a(n*2), n=0..37); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 03 2007
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MATHEMATICA
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s=0; lst={s}; Do[s+=n++ +6; AppendTo[lst, s], {n, 0, 7!, 8}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Nov 16 2008]
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CROSSREFS
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Cf. A007742, A033954, A046092, A054000.
Same as A033951 except start at 0.
Sequences from spirals: A001107, A002939, A007742, A033951, A033952, A033953, A033954, A033989, A033990, A033991, A002943, A033996, A033988.
Cf. A014105.
Cf. A007395, A016813 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 11 2009]
Adjacent sequences: A002940 A002941 A002942 this_sequence A002944 A002945 A002946
Sequence in context: A097811 A143711 A077539 this_sequence A068377 A009946 A094274
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KEYWORD
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nonn,easy,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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