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!)
 A225084 Triangle read by rows: T(n,k) is the number of compositions of n with maximal up-step k; n>=1, 0<=k
 1, 2, 0, 3, 1, 0, 5, 2, 1, 0, 7, 6, 2, 1, 0, 11, 12, 6, 2, 1, 0, 15, 26, 14, 6, 2, 1, 0, 22, 50, 33, 14, 6, 2, 1, 0, 30, 97, 72, 34, 14, 6, 2, 1, 0, 42, 180, 156, 77, 34, 14, 6, 2, 1, 0, 56, 332, 328, 173, 78, 34, 14, 6, 2, 1, 0, 77, 600, 681, 378, 177, 78, 34, 14, 6, 2, 1, 0, 101, 1078, 1393, 818, 393, 178, 78, 34, 14, 6, 2, 1, 0 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS T(n,k) is the number of compositions [p(1), p(2), ..., p(k)] of n such that max(p(j) - p(j-1)) == k. The first column is A000041 (partition numbers). Sum of first and second column is A003116. Sum of the first three columns is A224959. The second columns deviates from A054454 after the term 600. Row sums are A011782. LINKS Joerg Arndt and Alois P. Heinz, Rows n = 1..141, flattened EXAMPLE Triangle starts: 01: 1, 02: 2, 0, 03: 3, 1, 0, 04: 5, 2, 1, 0, 05: 7, 6, 2, 1, 0, 06: 11, 12, 6, 2, 1, 0, 07: 15, 26, 14, 6, 2, 1, 0, 08: 22, 50, 33, 14, 6, 2, 1, 0, 09: 30, 97, 72, 34, 14, 6, 2, 1, 0, 10: 42, 180, 156, 77, 34, 14, 6, 2, 1, 0, 11: 56, 332, 328, 173, 78, 34, 14, 6, 2, 1, 0, 12: 77, 600, 681, 378, 177, 78, 34, 14, 6, 2, 1, 0, 13: 101, 1078, 1393, 818, 393, 178, 78, 34, 14, 6, 2, 1, 0, 14: 135, 1917, 2821, 1746, 863, 397, 178, 78, 34, 14, 6, 2, 1, 0, 15: 176, 3393, 5660, 3695, 1872, 877, 398, 178, 78, 34, 14, 6, 2, 1, 0, ... The fifth row corresponds to the following statistics: #:  M   composition 01:  0  [ 1 1 1 1 1 ] 02:  1  [ 1 1 1 2 ] 03:  1  [ 1 1 2 1 ] 04:  2  [ 1 1 3 ] 05:  1  [ 1 2 1 1 ] 06:  1  [ 1 2 2 ] 07:  2  [ 1 3 1 ] 08:  3  [ 1 4 ] 09:  0  [ 2 1 1 1 ] 10:  1  [ 2 1 2 ] 11:  0  [ 2 2 1 ] 12:  1  [ 2 3 ] 13:  0  [ 3 1 1 ] 14:  0  [ 3 2 ] 15:  0  [ 4 1 ] 16:  0  [ 5 ] There are 7 compositions with no up-step (M=0), 6 with M=1, 2 with M=2, and 1 with M=3. MAPLE b:= proc(n, v) option remember; `if`(n=0, 1, add((p->       `if`(i seq(coeff(b(n, 0), x, i), i=0..n-1): seq(T(n), n=1..14);  # Alois P. Heinz, Feb 22 2014 MATHEMATICA b[n_, v_] := b[n, v] = If[n == 0, 1, Sum[Function[{p}, If[i

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 18 19:04 EST 2018. Contains 318243 sequences. (Running on oeis4.)