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!)
 A309805 Maximum number of nonattacking kings placeable on a hexagonal board with edge-length n in Glinski's hexagonal chess. 0
 1, 2, 7, 10, 19, 24, 37, 44, 61, 70, 91, 102, 127, 140, 169, 184, 217, 234, 271, 290, 331, 352, 397, 420, 469, 494, 547, 574, 631, 660, 721, 752, 817, 850, 919, 954, 1027, 1064, 1141, 1180, 1261, 1302, 1387, 1430, 1519, 1564, 1657, 1704, 1801, 1850, 1951, 2002 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Chess variants, Glinski's Hexagonal Chess Wikipedia, Hexagonal chess - GliĆski's hexagonal chess Index entries for linear recurrences with constant coefficients, signature (1,2,-2,-1,1). FORMULA a(n) = n^2 - floor(n/2) - floor(n/2)^2. From Stefano Spezia, Aug 18 2019 (Start) G.f.: - (1 + x + 3*x^2 + x^3)/((- 1 + x)^3*(1 + x)^2). E.g.f.: (1/8)*exp(-x)*(-1 + 2*x + exp(2*x)*(1 + 4*x + 6*x^2)). a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3) - a(n-4) + a(n-5) for n > 5. a(n) = (1/16)*(3 + (-1)^(1+2*n) - 4*n + 12*n^2 - 2*(-1)^n*(1 + 2*n)). a(2*n-1) = A003215(n). a(2*n) = A049450(n). (End) EXAMPLE a(1) = 1 .   o . a(2) = 2 .    . .   o . o    . . . a(3) = 7 .     o . o    . . . .   o . o . o    . . . .     o . o . a(4) = 10 .      . . . .     o . o . o    . . . . . .   o . o . o . o    . . . . . .     o . o . o      . . . . . PROG (PARI) a(n) = n^2 - (n\2) - (n\2)^2; \\ Andrew Howroyd, Aug 17 2019 CROSSREFS Cf. A003215, A049450. Sequence in context: A240469 A257335 A152211 * A125852 A155171 A049830 Adjacent sequences:  A309802 A309803 A309804 * A309806 A309808 A309809 KEYWORD nonn AUTHOR Sangeet Paul, Aug 17 2019 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 9 13:50 EST 2019. Contains 329877 sequences. (Running on oeis4.)