|
%I
%S 0,0,1,1,4,4,9,9,16,16,25,25,36,36,49,49,64,64,81,81,100,100,121,121,
%T 144,144,169,169,196,196,225,225,256,256,289,289,324,324,361,361,400,
%U 400,441,441,484,484,529,529,576,576
%N Squares repeated.
%C Also number of non-attacking kings on n-2 X n-2 board (cf. A030978). - Koksal Karakus (karakusk(AT)hotmail.com), May 27 2002
%C Maximum number of 2 X 2 tiles that fit on an n X n board. - _Jon Perry_, Aug 10 2003
%C (n)-(1) + (n-1) -(2) +(n-3)-(3)+ ... + (n-r) -(r)... n terms. e.g. 5-1+4-2+3=9 6-1+5-2+4-3=9 7-1+6-2+5-3+4 =16 8-1+7-2+6-3+5-4=16 - Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Jul 24 2005
%C The smallest possible number of white cells in a solution to an n X n nurikabe grid. [From _Tanya Khovanova_, Feb 24 2009]
%C (1 + x + 4x^2 + 4x^3 + 9x^4 + ...) = (1/(1-x))*(1 + 3x^2 + 5x^4 + 7x^6...) [From _Gary W. Adamson_, Apr 07 2010]
%C a(n) = A182579(n,n-2) for n > 1. [_Reinhard Zumkeller_, May 07 2012]
%H Vincenzo Librandi, <a href="/A008794/b008794.txt">Table of n, a(n) for n = 0..10000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/KingsProblem.html">Kings Problem.</a>
%F a(n)=[floor(n/2)]^2
%F a(n)=(2*n-1)*(-1)^n/8+(2*n^2-2*n +1)/8; a(n+1)=sum{k=0..n, k(1-(-1)^k)/2}. - _Paul Barry_, May 31 2003
%F a(n)={sqrt[sum_{j=0..n}(j+1)*(cos(j*Pi)+1)/2]-1}^2 with n>=0. - _Paolo P. Lava_, Dec 04 2006
%F a(n+2) = SUM(A109613(k)*A059841(n-k): 0<=k<=n). [From _Reinhard Zumkeller_, Dec 05 2009]
%p G.f.: x^2*(1+x^2)/((1-x^2)^2*(1-x)).
%o (MAGMA) [(2*n-1)*(-1)^n/8+(2*n^2-2*n +1)/8: n in [0..60]]; // Vincenzo Librandi, Aug 21 2011
%Y Cf. A086832.
%K nonn,easy
%O 0,5
%A _N. J. A. Sloane_.
|
