login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A036369 Number of asymmetric orthoplex n-ominoes in n-2 space 0
0, 0, 2, 10, 33, 101, 277, 754, 1972, 5134, 13145, 33563, 85048, 215075, 541887, 1363376, 3423537, 8588521, 21522243, 53898911, 134895022, 337467395, 843924068, 2109897826, 5273789335, 13180026621, 32934865984 (list; graph; refs; listen; history; text; internal format)
OFFSET

4,3

COMMENTS

Orthoplex polyominoes are multidimensional polyominoes that do not extend more than two units along any axis.

LINKS

Table of n, a(n) for n=4..30.

FORMULA

(A^2(x)-A(x^2))^2/8-A^2(x^2)/4+A(x^4)/4 +A^5(x)/(2-2A(x)) -A(x)A^2(x^2)/(2-2A(x^2)) where A(x) is generating function for rooted identity trees with n nodes.

EXAMPLE

2 asymmetric hexominoes in 2^4 space

MATHEMATICA

sa[ n_, k_ ] := sa[ n, k ]=a[ n+1-k, 1 ]+If[ n<2k, 0, -sa[ n-k, k ] ]; a[ 1, 1 ] := 1;

a[ n_, 1 ] := a[ n, 1 ]=Sum[ a[ i, 1 ]sa[ n-1, i ]i, {i, 1, n-1} ]/(n-1);

a[ n_, k_ ] := a[ n, k ]=Sum[ a[ i, 1 ]a[ n-i, k-1 ], {i, 1, n-1} ];

Table[ a[ i, 4 ]/8+Sum[ a[ i, j ], {j, 5, i} ]/2-If[ OddQ[ i ], 0, a[ i/2, 2 ]/8

-If[ OddQ[ i/2 ], 0, a[ i/4, 1 ]/4 ]+Sum[ a[ i/2, j ], {j, 3, i/2} ]/2 ]

-Sum[ a[ j, 1 ]a[ i-2j, 2 ]/4+Sum[ If[ OddQ[ k ], a[ j,

(k-1)/2 ]a[ i-2j, 1 ], 0 ], {k, 5, i} ]/2, {j, 1, (i-1)/2} ], {i, 4, 30} ]

CROSSREFS

Cf. A004111, A036366.

Sequence in context: A316644 A080668 A062453 * A294667 A240407 A043004

Adjacent sequences:  A036366 A036367 A036368 * A036370 A036371 A036372

KEYWORD

easy,nice,nonn

AUTHOR

Robert A. Russell

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified August 26 00:35 EDT 2019. Contains 326324 sequences. (Running on oeis4.)