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 A036368 Number of chiral orthoplex n-ominoes in n-2 space. 0
 0, 0, 4, 14, 37, 110, 324, 888, 2368, 6336, 16874, 44414, 116181, 303362, 790157, 2051880, 5317599, 13764133, 35586766, 91910082, 237183164, 611701614, 1576773162, 4062606255, 10463699696, 26942811809, 69358469092 (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 G.f.: (C^2(x) + C(-x^2))^2/8 - C^2(-x^2)/4 - C(-x^4)/4 + C^5(x)/(2-2C(x)) - (C(x)+C(-x^2))*C^2(-x^2)/(2-2C(-x^2)) where C(x) is the generating function for chiral n-ominoes in n-1 space, one cell labeled in A045648. EXAMPLE a(6)=4 because there are 4 pairs of chiral hexominoes in 2^4 space. MATHEMATICA sc[ n_, k_ ] := sc[ n, k ]=c[ n+1-k, 1 ]+If[ n<2k, 0, sc[ n-k, k ](-1)^k ]; c[ 1, 1 ] := 1; c[ n_, 1 ] := c[ n, 1 ]=Sum[ c[ i, 1 ]sc[ n-1, i ]i, {i, 1, n-1} ]/(n-1); c[ n_, k_ ] := c[ n, k ]=Sum[ c[ i, 1 ]c[ n-i, k-1 ], {i, 1, n-1} ]; Table[ c[ i, 4 ]/8+Sum[ c[ i, j ], {j, 5, i} ]/2-If[ OddQ[ i ], 0, c[ i/2, 2 ](-1)^(i/2)/8+If[ OddQ[ i/2 ], 0, c[ i/4, 1 ](-1)^(i/4)/4 ] +Sum[ c[ i/2, j ](-1)^(i/2), {j, 3, i/2} ]/2 ]+Sum[ c[ j, 1 ]c[ i-2j, 2 ](-1)^j/4 -Sum[ If[ OddQ[ k ], c[ j, (k-1)/2 ]c[ i-2j, 1 ](-1)^j/2, 0 ], {k, 5, i} ], {j, 1, (i-1)/2} ], {i, 4, 30} ] CROSSREFS Cf. A045648, A036367. Sequence in context: A192974 A187428 A316878 * A006071 A086954 A111583 Adjacent sequences:  A036365 A036366 A036367 * A036369 A036370 A036371 KEYWORD easy,nice,nonn AUTHOR STATUS approved

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Last modified May 9 22:09 EDT 2021. Contains 343746 sequences. (Running on oeis4.)