This site is supported by donations to The OEIS Foundation.

 Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing. Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A274616 Maximal number of non-attacking queens on a right triangular board with n cells on each side. 6
 0, 1, 1, 2, 2, 3, 4, 5, 5, 6, 7, 7, 8, 9, 9, 10, 11, 11, 12, 13, 13, 14, 15, 15, 16, 17, 17, 18, 19, 19, 20, 21, 21, 22, 23, 23, 24, 25, 25, 26, 27, 27, 28, 29, 29, 30, 31, 31, 32, 33, 33, 34, 35, 35, 36, 37, 37, 38, 39, 39, 40, 41, 41, 42, 43, 43, 44, 45, 45, 46, 47, 47 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS This sequence was mentioned by R. K. Guy in the first comment in A004396. REFERENCES Paul Vanderlind, Richard K. Guy, and Loren C. Larson, The Inquisitive Problem Solver, MAA, 2002. See Problem 252, pages 67, 87, 198 and 276. LINKS Colin Barker, Table of n, a(n) for n = 0..1000 F. Michel Dekking, Jeffrey Shallit, and N. J. A. Sloane, Queens in exile: non-attacking queens on infinite chess boards, arXiv:1907.09120, July 2019 Gabriel Nivasch and Eyal Lev, Nonattacking Queens on a Triangle, Mathematics Magazine, Vol. 78, No. 5 (Dec., 2005), pp. 399-403. Index entries for linear recurrences with constant coefficients, signature (1,0,1,-1). FORMULA Except for n=4, this is round(2n/3). From Colin Barker, Jul 02 2016: (Start) a(n) = a(n-1) + a(n-3) - a(n-4) for n>5. G.f.: x*(1+x^2-x^3)*(1+x^4)/((1-x)^2*(1+x+x^2)). (End) a(n) = 2*(3*n + sqrt(3)*sin((2*Pi*n)/3)) / 9. - Colin Barker, Mar 08 2017 EXAMPLE n=3: OOX XO O n=4: OOOX OXO OO O n=5: OOOOX OOXO XOO OO O MATHEMATICA CoefficientList[Series[x*(1 +x^2 -x^3)*(1 +x^4)/((1-x)^2*(1+x+x^2)), {x, 0, 50}], x] (* G. C. Greubel, Jul 03 2016 *) PROG (PARI) concat(0, Vec(x*(1+x^2-x^3)*(1+x^4)/((1-x)^2*(1+x+x^2)) + O(x^100))) \\ Colin Barker, Jul 02 2016 CROSSREFS Cf. A000170, A004396, A287864. Sequence in context: A156351 A057561 A064726 * A257175 A210357 A057359 Adjacent sequences:  A274613 A274614 A274615 * A274617 A274618 A274619 KEYWORD nonn,easy AUTHOR Rob Pratt and N. J. A. Sloane, Jul 01 2016 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 13 06:26 EST 2019. Contains 329968 sequences. (Running on oeis4.)