cp's OEIS Frontend

A233735 G.f.: x^3*(x^21 - x^20 - x^11 + x^10 + x^9 - x^8 + x^6 - x^5 + x^3 + x^2 - x + 1) / ((1-x^5) * (1-x)^2).

%I A233735 #40 Jan 09 2018 02:53:21
%S A233735 0,0,0,1,1,2,4,6,8,10,13,16,20,25,29,34,39,45,52,58,65,72,80,88,96,
%T A233735 105,114,124,134,144,155,166,178,190,202,215,228,242,256,270,285,300,
%U A233735 316,332,348,365,382,400,418,436,455,474,494,514,534
%N A233735 G.f.: x^3*(x^21 - x^20 - x^11 + x^10 + x^9 - x^8 + x^6 - x^5 + x^3 + x^2 - x + 1) / ((1-x^5) * (1-x)^2).
%C A233735 The second differences repeat with period 1,0,1,0,0 for n >= 20.
%C A233735 a(n) is a lower bound on A085577(n-2). The Ngaokrajang link shows arrangements of a(n) Greek crosses in an n X n grid. Note that a(11)=16, whereas A085577(9)=17, so the bound is not always tight. - _N. J. A. Sloane_, Apr 19 2015
%H A233735 G. C. Greubel, <a href="/A233735/b233735.txt">Table of n, a(n) for n = 0..1000</a>
%H A233735 Kival Ngaokrajang, <a href="/A233735/a233735_2.pdf">Packings of a(n) Greek crosses.</a> [Note that it is possible to pack 17 Greek crosses into an 11 X 11 grid (see A085577), so these arrangements are not always optimal. - _N. J. A. Sloane_, Apr 19 2015]
%H A233735 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,0,0,1,-2,1)
%t A233735 CoefficientList[Series[x^3*(x^21 - x^20 - x^11 + x^10 + x^9 - x^8 + x^6 - x^5 + x^3 +x^2 - x + 1)/((1 - x^5)*(1 - x)^2), {x, 0, 50}], x] (* _G. C. Greubel_, Jan 08 2018 *)
%o A233735 (PARI) x='x+O('x^50); Vec(x^3*(x^21 - x^20 - x^11 + x^10 + x^9 - x^8 + x^6 - x^5 + x^3 +x^2 - x + 1)/((1 - x^5)*(1 - x)^2)) \\ _G. C. Greubel_, Jan 08 2018
%Y A233735 Cf. A085576, A085577, A233035, A233036.
%K A233735 nonn,easy
%O A233735 0,6
%A A233735 _Kival Ngaokrajang_, Dec 15 2013
%E A233735 Entry revised by _N. J. A. Sloane_, Apr 19 2015. The new definition is a g.f. found by _Ralf Stephan_ on Dec 17 2013. The old definition was wrong.