A007220 Almost-convex polygons of perimeter 2n on square lattice. (Formerly M3692)

4, 60, 588, 4636, 31932, 200364, 1174492, 6538492, 34965772, 181084796, 913687100, 4511834156, 21880671292, 104497300828, 492527133804, 2295081478492, 10588446843324, 48422608206348, 219723559153052, 990104070700956, 4433734940648588

Offset

6,1

References

I. G. Enting, A. J. Guttmann, L. B. Richmond and N. C. Wormald, Enumeration of almost-convex polygons on the square lattice, Random Structures Algorithms 3 (1992), 445-461.

K. Y. Lin, Number of almost-convex polygons on the square lattice, J. Phys. A: Math. Gen. 25 (1992), 1835-1842.

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=6..26.

Formula

G.f. 16*x^3*A / ((1-x) * (1-4*x)^(5/2)) + 4*x^3*B / ((1-x) * (1-3*x+x^2) * (1-4*x)^3) where A = 1 - 9*x + 25*x^2 - 23*x^3 + 3*x^4 and B = -4 + 56*x - 300*x^2 + 773*x^3 - 973*x^4 + 535*x^5 - 90*x^6 + 24*x^7 [from Lin]. - Sean A. Irvine, Nov 21 2017

Crossrefs

Sequence in context: A366690 A002060 A247739 * A034866 A055315 A013482

Adjacent sequences: A007217 A007218 A007219 * A007221 A007222 A007223

Keyword

nonn

Author

Simon Plouffe

Extensions

More terms from Sean A. Irvine, Nov 21 2017

Status

approved