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Let T(n,d) = number of distinct d-dimensional polyominoes (or polycubes) with n cells (A049429, A049430); sequence gives Sum_{d} T(n,d).
(Formerly M1775)
8

%I M1775 #24 Jan 31 2022 01:40:29

%S 1,1,2,7,26,153,1134,11050,128987,1765252,27418060

%N Let T(n,d) = number of distinct d-dimensional polyominoes (or polycubes) with n cells (A049429, A049430); sequence gives Sum_{d} T(n,d).

%C These are free polyominoes, meaning that they are counted up to rotation, reflection, and translation. - _Peter Kagey_, Apr 30 2020

%D Dan Hoey, Bill Gosper and Richard C. Schroeppel, Discussions in Math-Fun Mailing list, circa Jul 13 1999.

%D W. F. Lunnon, personal communication.

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H R. C. Schroeppel, <a href="http://www.experimentalmath.info/workshop2004/schroeppel-talk.pdf">A few mathematical experiments</a>

%Y Row sums of A049429 or A049430.

%K nonn,nice,hard,more

%O 1,3

%A _N. J. A. Sloane_

%E a(9) from Richard C. Schroeppel

%E a(10) and a(11) from _Peter Kagey_, Apr 30 2020, based on the rows John Niss Hansen added to A049430