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 A125104 Triangle read by rows counting compositions (ordered partitions) by minimal part size. 1
 1, 1, 1, 1, 0, 3, 1, 0, 1, 6, 1, 0, 0, 2, 13, 1, 0, 0, 1, 3, 27, 1, 0, 0, 0, 2, 5, 56, 1, 0, 0, 0, 1, 2, 9, 115, 1, 0, 0, 0, 0, 2, 3, 15, 235, 1, 0, 0, 0, 0, 1, 2, 5, 25, 478, 1, 0, 0, 0, 0, 0, 2, 2, 8, 42, 969, 1, 0, 0, 0, 0, 0, 1, 2, 3, 12, 70, 1959, 1, 0, 0, 0, 0, 0, 0, 2, 2, 5, 18, 116, 3952, 1, 0, 0, 0, 0, 0, 0, 1, 2, 2, 8, 27, 192, 7959, 1, 0, 0, 0, 0, 0, 0, 0, 2, 2, 3, 11, 41, 317, 16007 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 COMMENTS The diagonals of this array can be generated from Table A099238 as follows: A000079 - A000045 = [1, 2, 4, 8, 16, 32, ...] - [0, 1, 1, 2, 3, 5, ...] = [1, 1, 3, 6, 13, 27, ...] = A099036, A000045 - A000930, A000930 - A003269, A003269 - A003520, etc. LINKS EXAMPLE Row 4 of the array is (1, 0, 1, 6) because there are six compositions with minimum part of size one: 1111, 31, 13, 211, 121, 112; one of size two: 22; none of size three; and 1 of size four: 4. Triangle (after 45-degree counterclockwise rotation) begins: 1 1 3 6 13 27 56 115 235 478 969 1959 3952 7959 .1 0 1 2 3 5 9 15 25 42 70 116 192 ..1 0 0 1 2 2 3 5 8 12 18 27 ...1 0 0 0 1 2 2 2 3 5 8 ....1 0 0 0 0 1 2 2 2 2 .....1 0 0 0 0 0 1 2 2 ......1 0 0 0 0 0 0 1 .......1 0 0 0 0 0 0 ........1 0 0 0 0 0 CROSSREFS Cf. A000079, A000045, A000930, A003269, A003520, A099036, A099238. Cf. A105147. Sequence in context: A121314 A119271 A323222 * A098157 A293617 A165253 Adjacent sequences:  A125101 A125102 A125103 * A125105 A125106 A125107 KEYWORD easy,nonn,tabl AUTHOR Alford Arnold, Nov 28 2006, corrected Nov 28 2006 EXTENSIONS Edited by N. J. A. Sloane, Dec 21 2006 More terms from Vladeta Jovovic, Jul 10 2007 STATUS approved

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Last modified February 29 09:35 EST 2020. Contains 332355 sequences. (Running on oeis4.)