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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

Table of n, a(n) for n=1..52.

Chess variants, Glinski's Hexagonal Chess

Wikipedia, Hexagonal chess - GliƄski'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

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Last modified December 9 13:50 EST 2019. Contains 329877 sequences. (Running on oeis4.)