OFFSET
1,3
LINKS
D. E. Knuth, Animals in a cage, Problem 10875, Amer. Math. Monthly, 110 (March 2003), 243-245.
R. J. Mathar, Corrigendum to "Polyomino Enumeration Results (Parkin et al, SIAM Fall Meeting 1967)" viXra:1905.0474 (2019)
R. Parkin, L. J. Lander, and D. R. Parkin, Polyomino Enumeration Results, presented at SIAM Fall Meeting, 1967, and accompanying letter from T. J. Lander (annotated scanned copy) page 9 (incorrect at n=15).
FORMULA
See Maple code.
MAPLE
A057051 := proc(n) if n mod 2 = 0 then binomial(2*n-2, n-1)+2^(n-2)-(3*n^2-2*n+8)/8; else binomial(2*n-2, n-1)+2^(n-2)-(3*n^2-4*n+9)/8+(1/2)*binomial(n-1, (n-1)/2); end if; end proc;
MATHEMATICA
f[n_] := If[EvenQ[n], Binomial[2n-2, n-1] + 2^(n-2) - (3n^2-2n+8)/8, Binomial[2n-2, n-1] + 2^(n-2) - (3n^2-4n+9)/8 + (1/2) Binomial[n-1, (n-1)/2]]; Table[f[n], {n, 1, 27}] (* Jean-François Alcover, Mar 18 2017, translated from Maple *)
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Mar 08 2003
STATUS
approved