A057753 - OEIS

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A057753

Total area of all polyominoes with perimeter 2n.

1

1, 2, 10, 27, 150, 641, 3796, 21525, 134863, 846159, 5464173, 35548106, 234007149, 1551388944, 10361158723

(list; graph; refs; listen; history; text; internal format)

OFFSET

2,2

LINKS

Table of n, a(n) for n=2..16.

Andrew Clarke, Isoperimetrical Polyominoes

Andrew Clarke, Picture from Andrew Clarke's page showing the polyominoes of perimeters 4, 6, 8 and 10.

EXAMPLE

a(2*n=4) = 1 with area 1: 1*1=1.

a(2*n=6) is 1 with area 2: 1*2=2.

a(2*n=8) is 2 with area 3, 1 with area 4: 2*3+4=10.

a(2*n=10) is 4 with area 4, 1 with area 5, 1 with area 6: 4*4+5+6=27.

a(2*n=12) = 11*5 +7*6 +4*7 +2*8 +1*9 = 150.

a(2*n=14) = 27*6 +21*7 +21*8+ 9*9 + 6*10 +1*11 + 1*12 = 641. - R. J. Mathar, Feb 18 2021

a(2*n=16) = 7*83 + 8*91 + 9*89 + 10*67 + 11*45 + 12*23 + 13*11 + 14*4 + 15*2 + 16*1. - John Mason, Feb 18 2021

CROSSREFS

Sequence in context: A327841 A196648 A220700 * A060515 A109723 A053594

Adjacent sequences: A057750 A057751 A057752 * A057754 A057755 A057756

KEYWORD

nonn,more

AUTHOR

N. J. A. Sloane, Nov 04 2000

EXTENSIONS

Link updated by William Rex Marshall, Dec 16 2009

Offset set to 2 by R. J. Mathar, Feb 18 2021

a(8) from John Mason, Feb 18 2021

a(9)-a(16) from John Mason, Sep 08 2022

STATUS

approved