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A005631 Bishops on a 2n+1 X 2n+1 board (see Robinson paper for details).
(Formerly M1628)
2
1, 2, 6, 18, 60, 200, 760, 2888, 11856, 48672, 215904, 957728, 4506304, 21203072, 105494400, 524880000, 2737670400, 14279148032, 77836363264, 424289980928, 2405307227136, 13635728197632, 80188215392256, 471566299547648, 2867649768509440, 17438513317683200 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

REFERENCES

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Table of n, a(n) for n=0..25.

R. W. Robinson, Counting arrangements of bishops, pp. 198-214 of Combinatorial Mathematics IV (Adelaide 1975), Lect. Notes Math., 560 (1976). [The sequence psi(2k+1).]

R. W. Robinson, Counting arrangements of bishops, pp. 198-214 of Combinatorial Mathematics IV (Adelaide 1975), Lect. Notes Math., 560 (1976). (Annotated scanned copy)

MAPLE

For Maple program see A005635.

MATHEMATICA

B[n_] := B[n] = Which[n == 0 || n == -2, 1, OddQ[n], B[n - 1], True, 2*B[n - 2] + (n - 2)*B[n - 4]];

a[n_] := B[n + 1]*B[n + 2]/2;

Table[a[n], {n, 0, 25}] (* Jean-François Alcover, Jul 23 2022, after Maple code for A123071 *)

CROSSREFS

Equals A123071(n)/2, n >= 1.

Cf. A005635.

Sequence in context: A358251 A002527 A005566 * A118677 A150043 A048117

Adjacent sequences:  A005628 A005629 A005630 * A005632 A005633 A005634

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from N. J. A. Sloane, Sep 28 2006

STATUS

approved

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Last modified November 26 04:03 EST 2022. Contains 358353 sequences. (Running on oeis4.)