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A007220 Almost-convex polygons of perimeter 2n on square lattice.
(Formerly M3692)
0
4, 60, 588, 4636, 31932, 200364, 1174492, 6538492, 34965772, 181084796, 913687100, 4511834156, 21880671292, 104497300828, 492527133804, 2295081478492, 10588446843324, 48422608206348, 219723559153052, 990104070700956, 4433734940648588 (list; graph; refs; listen; history; text; internal format)
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: A210425 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

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Last modified July 17 20:45 EDT 2019. Contains 325109 sequences. (Running on oeis4.)