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).

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, 105, 114, 124, 134, 144, 155, 166, 178, 190, 202, 215, 228, 242, 256, 270, 285, 300, 316, 332, 348, 365, 382, 400, 418, 436, 455, 474, 494, 514, 534

Offset: 0

Author

Kival Ngaokrajang, Dec 15 2013

Keywords

• nonn
• easy

Comments

The second differences repeat with period 1,0,1,0,0 for n >= 20.

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

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Kival Ngaokrajang, Packings of a(n) Greek crosses. [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]
• Index entries for linear recurrences with constant coefficients, signature (2,-1,0,0,1,-2,1)

Crossrefs

Cf. A085576, A085577, A233035, A233036.

Programs

Mathematica

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 *)

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

Extensions

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.