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 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 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 STATUS approved

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