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 A006772 Sum of spans of 2n-step polygons on square lattice. (Formerly M2971) 2
 0, 1, 3, 14, 70, 370, 2028, 11452, 66172, 389416, 2326202, 14070268, 86010680, 530576780, 3298906810, 20653559846, 130099026600, 823979294284, 5244162058026, 33523117491920, 215150177410088, 1385839069134800, 8956173544332434, 58056703069399056, 377396656568011618, 2459614847765495754, 16068572108927106202 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 REFERENCES N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS A. J. Guttmann and I. G. Enting, The size and number of rings on the square lattice, J. Phys. A 21 (1988), L165-L172. EXAMPLE From Andrey Zabolotskiy, Nov 09 2018: (Start) There are no 2-step polygons (conventionally). For n=2, the only 4-step polygon is a 1 X 1 square having span 1, so a(2)=1. For n=3, the only 6-step polygon is a 2 X 1 domino which can be rotated 2 ways having spans 2 and 1, so a(3) = 2+1 = 3. For n=4, there are the following 8-step polygons: a 3 X 1 stick which can be rotated 2 ways having spans 3 and 1; an L-tromino which can be rotated 4 ways, all having span 2; a 2 X 2 square, having span 2. So a(4) = 3 + 1 + 4*2 + 2 = 14. For n=5, there are the following 10-step polygons: a 4 X 1 stick which can be rotated 2 ways having spans 4 and 1; an L-tetromino which can be rotated 2 ways with span 2 and 2 more ways with span 3, plus reflections; a T-tetromino which can be rotated 2 ways with span 2 and 2 more ways with span 3; an S-tetromino which can be rotated 2 ways having spans 3 and 2, plus reflections; a 3 X 2 rectangle which can be rotated 2 ways having spans 3 and 2; a 3 X 2 rectangle without one of its angular squares having same counts as L-tetromino. So a(5) = 4 + 1 + 2 * 2*2*(2+3) + 2*(2+3) + 2*(3+2) + 3 + 2 = 70. (End) CROSSREFS Cf. A002931, A006773, A302336, A302337, A232103. Sequence in context: A270598 A001579 A327871 * A320421 A009020 A186765 Adjacent sequences:  A006769 A006770 A006771 * A006773 A006774 A006775 KEYWORD nonn AUTHOR EXTENSIONS Name corrected, more terms from Andrey Zabolotskiy, Nov 09 2018 STATUS approved

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Last modified January 26 17:17 EST 2020. Contains 331280 sequences. (Running on oeis4.)