A233760 -id:A233760 - cp's OEIS frontend

A233761 Number of toothpicks or D-toothpicks added at n-th stage in the structure of the D-toothpick "wide" triangle of A233760.

0, 1, 2, 2, 4, 2, 4, 6, 8, 2, 4, 6, 12, 14, 12, 14, 16, 2, 4, 6, 12, 14, 20, 22, 26, 22, 12, 18, 32, 38, 28, 30, 32, 2, 4, 6, 12, 14, 20, 22, 26, 22, 20, 30, 44, 62, 52, 46, 54, 38, 12, 18, 36, 46, 56, 62, 74, 74, 30, 42, 72, 86, 60, 62, 64, 2, 4, 6, 12

Offset: 0

Omar E. Pol, Dec 16 2013

Essentially the first differences of A233760.

			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;
2,4,6,12,14,12,14,16;
2,4,6,12,14,20,22,26,22,12,18,32,38,28,30,32;
2,4,6,12,14,20,22,26,22,20,30,44,62,52,46,54,38,12,18,36,46,56,62,74,74,30,42,72,86,60,62,64;
Right border gives A000079.

Cf. A000079, A011782, A139251, A220501, A220521, A233760, A233763, A233781.

a(2n) = A220521(2n); a(2n+1) = A220521(2n+1) - 2.

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

Original entry on oeis.org

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.

A233762 Number of toothpicks and D-toothpicks after n-th stage in the D-toothpick "narrow" triangle of the third kind, second version.

Original entry on oeis.org

0, 1, 3, 5, 9, 11, 15, 20, 28, 30, 34, 40, 52, 58, 64, 75, 91, 93, 97, 103, 115, 129, 145, 163, 187, 197, 205, 219, 247, 261, 277, 300, 332, 334, 338, 344, 356, 370, 386, 406, 438, 464, 484, 506, 546, 576, 616, 655, 703, 721, 729

Offset: 0

Omar E. Pol, Dec 15 2013

nonn

The structure is essentially the same as A220522 but here the borders do not contain D-toothpicks with exposed endpoints except the initial D-toothpick. The structure is one of the oblique wedges of several D-toothpick structures. For more information see A220500. The first differences (A233763) give the number of toothpicks or D-toothpicks added at n-th stage.

Cf. A139250, A220500, A220522, A233760, A233763.

cp's OEIS Frontend

A233761 Number of toothpicks or D-toothpicks added at n-th stage in the structure of the D-toothpick "wide" triangle of A233760.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula

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

Views

Author

Keywords

Comments

Links

Crossrefs

A233762 Number of toothpicks and D-toothpicks after n-th stage in the D-toothpick "narrow" triangle of the third kind, second version.

Views

Author

Keywords

Comments

Links

Crossrefs