A057753 Total area of all polyominoes with perimeter 2n.

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

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

Cf. A057730.

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