1,3

Row sums = A163312: (1, 3, 8, 17, 34, 64,...). Right border = A163267, Toothpick sequence for N=1. Next diagonal going to

the left = A139250, Toothpick sequence for N=2. Then 1, 4, 10, 19,... =

A162958, Toothpick sequence for N=3.

(Cf. A162958 for rules governing the generation of N-th Toothpick sequences

By way of example, (N+2), A139250. The generator is A160552, which uses

the multiplier "2". Then A160552 convolved with (1, 2, 2, 2,...) = A139250

the Toothpick sequence for N=2. Similarly, we create an array for Toothpick

sequences N=1, 2, 3,...etc = A163267, A139250, A162958,...; then take the

antidiagonals, creating triangle A163311

First few rows of the triangle =

1;

1, 2;

1, 3, 4;

1, 4, 7, 5;

1, 5, 10, 11, 7;

1, 6, 13, 19, 15, 10;

1, 7, 16, 29, 25, 23, 13;

1, 8, 19, 41, 37, 40, 35, 14;

1, 9, 22, 55 51, 61, 67, 43, 16;

1, 10, 25, 71, 67, 86, 109, 94, 47, 19;

1, 11, 28, 89, 85, 115, 161, 173, 100, 55, 22;

1, 12, 31, 109, 105, 148, 223, 286, 181, 115, 67, 25;

1, 13, 34, 131, 127, 185, 295, 439, 296, 205, 142, 79, 30;

1, 14, 37, 155, 151, 226, 377, 638, 451, 331, 253, 175, 95, 36;

...

A163267, A139250, A162958, A160552

Sequence in context: A085643 A132110 A039912 this_sequence A008949 A076832 A078925

Adjacent sequences: A163308 A163309 A163310 this_sequence A163312 A163313 A163314

nonn,tabl

Gary W. Adamson (qntmpkt(AT)yahoo.com), Jul 24 2009