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D-toothpick sequence of the second kind (see Comments lines for definition).
+10
37
0, 1, 5, 13, 29, 51, 75, 97, 137, 177, 209, 241, 297, 371, 467, 517, 605, 677, 709, 757, 829, 933, 1061, 1173, 1317, 1461, 1613, 1709, 1861, 2039, 2279, 2401, 2585, 2721, 2753, 2801, 2873, 2981, 3125, 3269, 3453, 3641, 3841, 4017, 4289, 4563, 4979, 5229
COMMENTS
Note that this structure is much more complex than A139250 and A160120. The structure contains a large number of distinct polygonal shapes. There are convex polygons and concave polygons, also there are symmetrical and asymmetrical polygons. Several of these polygons are also in the structure of A172310. The number of edges of the known polygons are 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 17, 20, 24. Is not known how many distinct types of polygons there are in the structure if n -> infinite. The sequences related with these polygons are A194276, A194277, A194278 and A194283. Note that the structure is not centered with respect to the axes X, Y. Also, for some polygons the area is not an integer. For symmetric versions of C. A. see A194432 and A194434.
CROSSREFS
Cf. A139250, A160120, A172310, A182838, A194271, A194276, A194277, A194278, A194440, A194441, A194442, A194443, A194444.
Known number of distinct polygonal shapes with n sides in the infinite D-toothpick structure of A194270.
+10
7
2, 4, 3, 6, 7, 2, 7, 7, 2, 3, 3, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1
Number of distinct polygonal shapes after n-th stage in the D-toothpick structure of A194270.
+10
6
0, 0, 0, 0, 1, 3, 4, 5, 6, 7, 9, 10, 10, 11, 13, 13, 14
Numbers n such that at stage n of A194270 appears for first time a new distinct polygonal shape in the structure.
+10
1
4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 16, 21
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