A233972 -id:A233972 - cp's OEIS frontend

A233970 Toothpick sequence on hexagonal net starting from the vertex of a 60-degree wedge (see Comments lines for precise definition).

0, 1, 3, 5, 9, 11, 15, 21, 29, 31, 35, 41, 51, 61, 69, 83, 99, 101, 105, 111, 121, 131, 141, 159, 183, 205, 213, 227, 249, 275, 291, 321, 353, 355, 359, 365, 375, 385, 395, 413, 437, 459, 469, 487, 515, 553, 581, 627, 683, 737, 745, 759, 781, 807

Offset: 0

Omar E. Pol, Dec 18 2013

nonn

Toothpicks are connected by their endpoints. The toothpicks placed in north direction are prohibited. The sequence gives the number of toothpicks after n-th stage in the structure. A233971 (the first differences) give the number of toothpicks added at n-th stage.
First differs from A169780 at a(24).
First differs from both A233764 and A233780 at a(25).

Cf. A139250, A161206, A161830, A169780, A182632, A182634, A182634, A182840, A233760, A233764, A233780, A233971, A233972.

A233971 Number of toothpicks added at n-th stage to the structure of A233970.

Original entry on oeis.org

0, 1, 2, 2, 4, 2, 4, 6, 8, 2, 4, 6, 10, 10, 8, 14, 16, 2, 4, 6, 10, 10, 10, 18, 24, 22, 8, 14, 22, 26, 16, 30, 32, 2, 4, 6, 10, 10, 10, 18, 24, 22, 10, 18, 28, 38, 28, 46, 56, 54, 8, 14, 22, 26, 22, 42, 56, 62, 16, 30, 46, 58, 32, 62, 64, 2, 4, 6, 10, 10

Offset: 0

Omar E. Pol, Dec 18 2013

Essentially the first differences of A233970.
First differs from A170905 at a(24).
First differs from both A233765 and A233781 at a(25).

			Written as an irregular triangle in which the row lengths is A011782 the sequence (starting from 1) begins:
1;
2;
2,4;
2,4,6,8;
2,4,6,10,10,8,14,16;
2,4,6,10,10,10,18,24,22,8,14,22,26,16,30,32;
2,4,6,10,10,10,18,24,22,10,18,28,38,28,46,56,54,8,14,22,26,22,42,56,62,16,30,46,58,32,62,64;
Right border gives A000079.

Cf. A000079, A011782, A139251, A161207, A161831, A170905, A182633, A182635, A182841, A233761, A233765, A233781, A233970, A233972.

cp's OEIS Frontend

A233970 Toothpick sequence on hexagonal net starting from the vertex of a 60-degree wedge (see Comments lines for precise definition).

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