Search: id:A002943
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%I A002943
%S A002943 0,6,20,42,72,110,156,210,272,342,420,506,600,702,812,930,
%T A002943 1056,1190,1332,1482,1640,1806,1980,2162,2352,2550,2756,
%U A002943 2970,3192,3422,3660,3906,4160,4422,4692,4970,5256,5550
%N A002943 2n(2n+1).
%C A002943 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.
%C A002943 Write 0,1,2,... in clockwise spiral; sequence gives numbers on one of 
               4 diagonals.
%C A002943 Twice second hexagonal numbers (Cf. A014105). - Omar E. Pol (info(AT)polprimos.com), 
               May 21 2008
%C A002943 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]
%D A002943 R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics. Addison-Wesley, 
               Reading, MA, 2nd ed., 1994, p. 99.
%H A002943 T. D. Noe, <a href="b002943.txt">Table of n, a(n) for n=0..1000</a>
%H A002943 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               QueensTourGraph.html">Queen's Tour Graph</a>
%F A002943 4n^2+2n.
%F A002943 a(n)=A014105(n)*2. - Omar E. Pol (info(AT)polprimos.com), May 21 2008
%F A002943 a(n)=8*n+a(n-1)-10 (with a(1)=0) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), 
               Nov 12 2009]
%e A002943 16 17 18 19 ...
%e A002943 15 4 5 6 ...
%e A002943 14 3 0 7 ...
%e A002943 13 2 1 8 ...
%e A002943 For n=2, a(2)=8*2+0-10=6; n=3, a(3)=8*3+6-10=20; n=4, a(4)=8*4+20-10=42 
               [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 12 2009]
%p A002943 a:=n->sum(n+1, j=1..n): seq(a(n*2), n=0..37); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               May 03 2007
%t A002943 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]
%Y A002943 Cf. A007742, A033954, A046092, A054000.
%Y A002943 Same as A033951 except start at 0.
%Y A002943 Sequences from spirals: A001107, A002939, A007742, A033951, A033952, 
               A033953, A033954, A033989, A033990, A033991, A002943, A033996, A033988.
%Y A002943 Cf. A014105.
%Y A002943 Cf. A007395, A016813 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), 
               Mar 11 2009]
%Y A002943 Sequence in context: A097811 A143711 A077539 this_sequence A068377 A009946 
               A094274
%Y A002943 Adjacent sequences: A002940 A002941 A002942 this_sequence A002944 A002945 
               A002946
%K A002943 nonn,easy,nice
%O A002943 0,2
%A A002943 N. J. A. Sloane (njas(AT)research.att.com).

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