This site is supported by donations to The OEIS Foundation.

 Annual Appeal: Please make a donation to keep the OEIS running. In 2018 we replaced the server with a faster one, added 20000 new sequences, and reached 7000 citations (often saying "discovered thanks to the OEIS"). Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A218577 Triangle read by rows: T(n,k) is the number of ascent sequences of length n with maximal element k-1. 7
 1, 1, 1, 1, 3, 1, 1, 7, 6, 1, 1, 15, 25, 11, 1, 1, 31, 90, 74, 20, 1, 1, 63, 301, 402, 209, 37, 1, 1, 127, 966, 1951, 1629, 590, 70, 1, 1, 255, 3025, 8869, 10839, 6430, 1685, 135, 1, 1, 511, 9330, 38720, 65720, 56878, 25313, 4870, 264, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS Row sums are A022493. Second column is A000225 (2^n - 1). Third column appears to be A000392 (Stirling numbers S(n,3)). Second diagonal (from the right) appears to be A006127 (2^n + n). LINKS Joerg Arndt and Alois P. Heinz, Rows n = 1..141, flattened (first 15 rows from Joerg Arndt) Mireille Bousquet-MÃ©lou, Anders Claesson, Mark Dukes, Sergey Kitaev, (2+2)-free posets, ascent sequences and pattern avoiding permutations, arXiv:0806.0666 [math.CO], 2008-2009. William Y. C. Chen, Alvin Y.L. Dai, Theodore Dokos, Tim Dwyer and Bruce E. Sagan, On 021-Avoiding Ascent Sequences, The Electronic Journal of Combinatorics Volume 20, Issue 1 (2013), #P76. EXAMPLE Triangle starts: 1; 1,    1; 1,    3,     1; 1,    7,     6,      1; 1,   15,    25,     11,      1; 1,   31,    90,     74,     20,      1; 1,   63,   301,    402,    209,     37,      1; 1,  127,   966,   1951,   1629,    590,     70,     1; 1,  255,  3025,   8869,  10839,   6430,   1685,   135,     1; 1,  511,  9330,  38720,  65720,  56878,  25313,  4870,   264,   1; 1, 1023, 28501, 164676, 376114, 444337, 292695, 99996, 14209, 521, 1; ... The 53 ascent sequences of length 5 are (dots for zeros): [ #]     ascent-seq.   #max digit [ 1]    [ . . . . . ]   0 [ 2]    [ . . . . 1 ]   1 [ 3]    [ . . . 1 . ]   1 [ 4]    [ . . . 1 1 ]   1 [ 5]    [ . . . 1 2 ]   2 [ 6]    [ . . 1 . . ]   1 [ 7]    [ . . 1 . 1 ]   1 [ 8]    [ . . 1 . 2 ]   2 [ 9]    [ . . 1 1 . ]   1 [10]    [ . . 1 1 1 ]   1 [11]    [ . . 1 1 2 ]   2 [12]    [ . . 1 2 . ]   2 [13]    [ . . 1 2 1 ]   2 [14]    [ . . 1 2 2 ]   2 [15]    [ . . 1 2 3 ]   3 [16]    [ . 1 . . . ]   1 [17]    [ . 1 . . 1 ]   1 [18]    [ . 1 . . 2 ]   2 [19]    [ . 1 . 1 . ]   1 [20]    [ . 1 . 1 1 ]   1 [21]    [ . 1 . 1 2 ]   2 [22]    [ . 1 . 1 3 ]   3 [23]    [ . 1 . 2 . ]   2 [24]    [ . 1 . 2 1 ]   2 [25]    [ . 1 . 2 2 ]   2 [26]    [ . 1 . 2 3 ]   3 [27]    [ . 1 1 . . ]   1 [28]    [ . 1 1 . 1 ]   1 [29]    [ . 1 1 . 2 ]   2 [...] [49]    [ . 1 2 3 . ]   3 [50]    [ . 1 2 3 1 ]   3 [51]    [ . 1 2 3 2 ]   3 [52]    [ . 1 2 3 3 ]   3 [53]    [ . 1 2 3 4 ]   4 There is 1 sequence with maximum zero, 15 with maximum one, etc., therefore the fifth row is 1, 15, 25, 11, 1. CROSSREFS Cf. A022493 (number of ascent sequences), A137251 (ascent sequences with k ascents), A175579 (ascent sequences with k zeros). Cf. A218579 (ascent sequences with last zero at position k-1), A218580 (ascent sequences with first occurrence of the maximal value at position k-1), A218581 (ascent sequences with last occurrence of the maximal value at position k-1). Sequence in context: A154959 A080417 A008277 * A193387 A185982 A263858 Adjacent sequences:  A218574 A218575 A218576 * A218578 A218579 A218580 KEYWORD nonn,tabl AUTHOR Joerg Arndt, Nov 03 2012 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 11 22:04 EST 2018. Contains 318052 sequences. (Running on oeis4.)