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A173033
Second diagonal under the main diagonal in A172119 written in a square (see comment).
18
1, 4, 12, 28, 60, 124, 252, 508, 1020, 2044, 4092, 8188, 16380, 32764, 65532, 131068, 262140, 524284, 1048572, 2097148, 4194300, 8388604, 16777212, 33554428, 67108860, 134217724, 268435452, 536870908, 1073741820, 2147483644, 4294967292, 8589934588, 17179869180
OFFSET
0,2
COMMENTS
The Granvik array of A172119 is here written in "square": 1 :: 1 :: 1 :: 1 :: 1 :: 1 :: 1 :: 1 :: 1 :: 1 // 1 :: 2 :: 2 :: 2 :: 2 :: 2 :: 2 :: 2 :: 2 :: 2 // 1 :: 3 :: 4 :: 4 :: 4 :: 4 :: 4 :: 4 :: 4 :: 4 // 1 :: 4 :: 7 :: 8 :: 8 :: 8 :: 8 :: 8 :: 8 :: 8 // 1 :: 5 :: 12 :: 15 :: 16 :: 16 :: 16 :: 16 :: 16 :: 16 // 1 :: 6 :: 20 :: 28 :: 31 :: 32 :: 32 :: 32 :: 32 :: 32 // 1 :: 7 :: 33 :: 52 :: 60 :: 63 :: 64 :: 64 :: 64 :: 64 // 1 :: 8 :: 54 :: 96 :: 116 :: 124 :: 127 :: 128 :: 128 :: 128 // 1 :: 9 :: 88 :: 177 :: 224 :: 244 :: 252 :: 255 :: 256 :: 256 //
For n>0 a(n) is also the number of ways to place n^2 non-attacking kings on a 2n X 2n toroidal chessboard. - Vaclav Kotesovec, Aug 28 2011
The number of n-step self-avoiding walks on a 2D square lattice where no step is to a lattice point closer to the origin than the current point. - Scott R. Shannon, Dec 15 2023
LINKS
Vaclav Kotesovec, Non-attacking chess pieces, 6th ed, 2013, p. 215.
FORMULA
G.f.: 4/(1-2*x) - 4/(1-x) + 1.
a(n) = 2^(n+2) - 4 for n>=1, a(0)=1.
a(n) = A028399(n+2), n>0. - R. J. Mathar, Feb 21 2010
a(n) = A240951(n+3) - 4. - Omar E. Pol, Feb 17 2015
a(n) = 2*a(n-1) + 4 for n>1. - J. Conrad, Nov 01 2015
a(n) = 3*a(n-1)-2*a(n-2) for n>2. - Colin Barker, Nov 03 2015
E.g.f.: (1 - 2*exp(x))^2. - Stefano Spezia, May 03 2023
EXAMPLE
a(3) = 2^5 - 4 = 32 - 4 = 28.
MAPLE
taylor(4/(1-2*z)-4/(1-z)+1, z=0, 31);
MATHEMATICA
CoefficientList[Series[4 / (1 - 2 x) - 4 / (1 - x) + 1, {x, 0, 60}], x] (* Vincenzo Librandi, May 29 2013 *)
PROG
(PARI) x='x+O('x^50); Vec(4/(1-2*x)-4/(1-x)+1) \\ Altug Alkan, Nov 02 2015
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Richard Choulet, Feb 07 2010
STATUS
approved