0,2

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]

R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics. Addison-Wesley, Reading, MA, 2nd ed., 1994, p. 99.

T. D. Noe, Table of n, a(n) for n=0..1000

Eric Weisstein's World of Mathematics, Queen's Tour Graph

4n^2+2n.

a(n)=A014105(n)*2. - Omar E. Pol (info(AT)polprimos.com), May 21 2008

a(n)=8*n+a(n-1)-10 (with a(1)=0) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 12 2009]

16 17 18 19 ...

15 4 5 6 ...

14 3 0 7 ...

13 2 1 8 ...

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]

a:=n->sum(n+1, j=1..n): seq(a(n*2), n=0..37); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 03 2007

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]

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]

Sequence in context: A097811 A143711 A077539 this_sequence A068377 A009946 A094274

Adjacent sequences: A002940 A002941 A002942 this_sequence A002944 A002945 A002946

nonn,easy,nice

N. J. A. Sloane (njas(AT)research.att.com).