0,2

Write 1,2,3,4,... in a hexagonal spiral around 0, then a(n) is the sequence found by reading the line from 0 in the direction 0,4,... - Floor van Lamoen (fvlamoen(AT)hotmail.com), Jul 21 2001. The spiral begins:

......16..15..14

....17..5...4...13

..18..6...0...3...12

19..7...1...2...11..26

..20..8...9...10..25

....21..22..23..24

Number of edges in the join of the complete bipartite graph of order 2n and the cycle graph of order n, K_n,n * C_n - Roberto E. Martinez II (remartin(AT)fas.harvard.edu), Jan 07 2002

The average of the first n elements starting from a(1) is equal to (n+1)^2. - Mario Catalani (mario.catalani(AT)unito.it), Apr 10 2003

If Y is a 4-subset of an n-set X then, for n>=4, a(n-4) is the number of (n-4)-subsets of X having either one element or two elements in common with Y. - Milan R. Janjic (agnus(AT)blic.net), Dec 28 2007

The maximum possible sum of numbers in an N x N standard Minesweeper grid. [From Dmitry Kamenetsky (dkamen(AT)rsise.anu.edu.au), Dec 14 2008]

L. B. W. Jolley, "Summation of Series", Dover Publications, 1961, p. 12. [Jolley]

a(n) = n*(3*n+1). G.f.: A(x) = 2*x*(2+x)/(1-x)^3.

4 + 14 + 30 + 52 + 80 +...n terms = n*(n+1)^2. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Dec 20 2006

a(n) = A005449(n)*2. [From Omar E. Pol (info(AT)polprimos.com), Dec 18 2008]

a(n)=6*n+a(n-1)-8 (with a(1)=0) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 08 2009]

Contribution from Dmitry Kamenetsky (dkamen(AT)rsise.anu.edu.au), Dec 14 2008, with slight rewording by Raymond Martineau (mart0258(AT)yahoo.com), Dec 16 2008: (Start)

For an N x N Minesweeper grid the highest sum of numbers is (N-1)(3*N-2). This is achieved by filling every second row with mines (shown as 'X'). For example, when N=5 the best grids are:

XXXXX

46664

XXXXX

46664

XXXXX

and

23332

XXXXX

46664

XXXXX

23332

Both giving a total of 52. (End)

For n=2, a(2)=6*2+0-8=4; n=3, a(3)=6*3+4-8=14; n=4, a(4)=6*4+14-8=30 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 08 2009]

a:=n->sum(2*(n+j), j=1..n): seq(a(n), n=0..44); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 26 2008

s=0; lst={s}; Do[s+=n+++4; AppendTo[lst, s], {n, 0, 7!, 6}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Nov 16 2008]

lst={}; Do[AppendTo[lst, (((n+1)^3)-((n+1)^2))-((n^3)-(n^2))], {n, 0, 5!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Mar 01 2009]

Cf. A000567.

Cf. A005449, A033580, A049450.

Sequence in context: A130439 A033690 A103779 this_sequence A079776 A117109 A140063

Adjacent sequences: A049448 A049449 A049450 this_sequence A049452 A049453 A049454

nonn,easy,new

Joe Keane (jgk(AT)jgk.org).