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A355052
Number of oriented multidimensional n-ominoes with cell centers determining n-3 space.
5
1, 17, 131, 709, 3350, 14337, 57507, 218746, 803384, 2870707, 10044838, 34548917, 117224825, 393290329, 1307200931, 4310348599, 14116544717, 45959805027, 148860350902, 479938536114, 1541025955958, 4929773150983
OFFSET
4,2
COMMENTS
Multidimensional polyominoes are connected sets of cells of regular tilings with Schläfli symbols {oo}, {4,4}, {4,3,4}, {4,3,3,4}, etc. Each tile is a regular orthotope (hypercube). This sequence is obtained using the first formula below. For oriented polyominoes, chiral pairs are counted as two.
LINKS
W. F. Lunnon, Counting multidimensional polyominoes. Computer Journal 18 (1975), no. 4, pp. 366-367.
FORMULA
a(n) = A355053(n) + A355054(n) = 2*A355053(n) - A355055(n) = 2*A355054(n) + A355055(n).
a(n) = A195738(n,n-3), the third diagonal of Lunnon's DR array.
EXAMPLE
a(4)=1 because there is just one tetromino (with four cells aligned) in 1-space. a(5)=17 because there are 5 achiral and 6 chiral pairs of pentominoes in 2-space, excluding the 1-D straight pentomino.
CROSSREFS
Cf. A355053 (unoriented), A355054 (chiral), A355055 (achiral) A355056 (asymmetric), A191092 (fixed), A355047 (orthoplex), A195738 (Lunnon's DR).
Sequence in context: A142676 A087191 A158959 * A259418 A253416 A275483
KEYWORD
nonn,easy
AUTHOR
Robert A. Russell, Jun 16 2022
STATUS
approved