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 A342968 Irregular triangle read by rows: T(n,k) is the number of n+2-sided polygons with the property that one makes k turns on itself while following its edges. 2
 1, 0, 1, 2, 1, 5, 6, 1, 24, 28, 8, 119, 183, 57, 1, 832, 1209, 432, 47, 6255, 9514, 3760, 630, 1, 54380, 82636, 36352, 7828, 244, 515284, 812714, 383648, 94997, 7756, 1, 5454624, 8727684, 4377888, 1243482, 153536, 1186 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS Polygons that differ by rotation or reflection are counted separately. By "n+2-sided polygons" we mean the polygons that can be drawn by connecting n+2 equally spaced points on a circle (possibly self-intersecting). T(0,0)=1 by convention. To compute the number of turns, follow the edges of the polygon, and add the angles of rotation: positive if turning left, negative if turning right. Then take the absolute value of the sum (see illustration). LINKS Ludovic Schwob, Illustration of T(5,k), 0 <= k <= 3 FORMULA T(2*n-1,n)=1 for all n >= 1: the only solution is the polygon with SchlĂ¤fli symbol {2*n+1/n}. EXAMPLE Triangle begins:      1;      0,    1;      2,    1;      5,    6,    1;     24,   28,    8;    119,  183,   57,   1; CROSSREFS Row sums give A001710(n+1) (number of polygons with n+2 sides). Sequence in context: A302595 A113345 A078123 * A323312 A231774 A209170 Adjacent sequences:  A342965 A342966 A342967 * A342969 A342970 A342972 KEYWORD nonn,tabf,more AUTHOR Ludovic Schwob, Apr 01 2021 STATUS approved

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Last modified July 29 02:36 EDT 2021. Contains 346340 sequences. (Running on oeis4.)