A236535 -id:A236535 - cp's OEIS frontend

A236754 Number of irregular spirals (non-expanded loop) appearing with n center points.

1, 0, 6, 8, 120, 0, 5040, 4608, 362880, 0, 39916800

Offset: 1

Kival Ngaokrajang, Jan 30 2014

See A236535 for construction rule.

Conjecture: (1) For odd n all forms are non-expanded loops and equal to n!. (2) For n mod 4 = 0, there are both non-expanded loops and expanded spirals.

Kival Ngaokrajang, Illustration of irregular spirals, center points = 1..6
Kival Ngaokrajang, Small Basic program

Cf. A014105 (2 center points); A234902, A234903, A234904, A236535 (3 center points); A235088, A235089 (4 center points); A236326, A236327 (5 center points).

A236755 Number of irregular spiral (expanded spiral) appearing with n center points.

Original entry on oeis.org

0, 2, 0, 16, 0, 720, 0, 35712, 0, 3628800, 0

Offset: 1

Kival Ngaokrajang, Jan 30 2014

See A236535 for construction rule.

Conjecture: (1) For even n; except n mod 4 = 0; all forms are expanded spirals and equal to n!. (2) For n mod 4 = 0, there are both non-expanded loops and expanded spirals.

Kival Ngaokrajang, Illustration of irregular spirals, center points = 1..6
Kival Ngaokrajang, Small Basic program

Cf. A014105 (2 center points); A234902, A234903, A234904, A236535 (3 center points); A235088, A235089 (4 center points); A236326, A236327 (5 center points).

cp's OEIS Frontend

A236754 Number of irregular spirals (non-expanded loop) appearing with n center points.

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