A370766
Number of signed permutations of length n with adjacent elements differing by more than 1.
Original entry on oeis.org
1, 2, 4, 20, 156, 1540, 18268, 253380, 4024220, 72006788, 1433150940, 31402068292, 751081569820, 19471227247620, 543821277818972, 16278774958879940, 519912803924769948, 17646698226141369220, 634307673944308523740, 24070514898945667594308
Offset: 0
In the following examples, the number of assignments of signs to each unsigned permutation is shown in parenthesis.
a(2) = 4: 12(2), 21(2). Total is 2 + 2 = 4.
a(3) = 20: 123(2), 132(4), 213(4), 231(4), 312(4), 321(2).
A370767
Number of signed permutations of length n+1 with adjacent elements differing by more than 1 and whose first element is 1.
Original entry on oeis.org
1, 1, 3, 17, 139, 1401, 16867, 236513, 3787707, 68219081, 1364931859, 30037136433, 721044433387, 18750182814233, 525071095004739, 15753703863875201, 504159100060894747, 17142539126080474473, 617165134818228049267, 23453349764127439545041
Offset: 0
In the following examples, the number of assignments of signs to each unsigned permutation is shown in parenthesis.
a(2) = 3: 123(1), 132(2). Total is 1 + 2 = 3.
a(3) = 17: 1234(1), 1243(2), 1324(4), 1342(4), 1423(4), 1432(2).
A370769
Number of achiral unicursal star polygons (no edge joins adjacent vertices) that can be formed by connecting the vertices of a regular n-gon.
Original entry on oeis.org
0, 0, 0, 0, 1, 1, 5, 11, 49, 123, 521, 1583, 6581, 23239, 95509, 384771, 1570265, 7106995, 28869825, 145034327, 587270877, 3242792607, 13100475021, 78866628011, 318067071169, 2073381189259, 8350998470777, 58602568320255, 235794888434053, 1772311322357623
Offset: 1
Cf.
A231091 (stars up to rotation),
A370459 (up to rotation and reflection).
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Ro(n)=-(-1)^n + subst(serlaplace(polcoef(((1 - x)^2)/(2*(1 + x)*(1 + (1 - 2*y)*x + 2*y*x^2)) + O(x*x^n), n)), y, 1)
Re(n)=subst(serlaplace(polcoef((1 - 3*x)/(8*(1 + (1 - 2*y)*x + 2*y*x^2)) + O(x*x^n), n)), y, 1)
a(n) = if(n < 3, 0, if(n % 2, Ro(n\2), Re(n/2)))
Showing 1-3 of 3 results.
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