The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A270236 Triangle T(n,p) read by rows: the number of occurrences of p in the restricted growth functions of length n. 17
 1, 3, 1, 9, 5, 1, 30, 21, 8, 1, 112, 88, 47, 12, 1, 463, 387, 253, 97, 17, 1, 2095, 1816, 1345, 675, 184, 23, 1, 10279, 9123, 7304, 4418, 1641, 324, 30, 1, 54267, 48971, 41193, 28396, 13276, 3645, 536, 38, 1, 306298, 279855, 243152, 183615, 102244, 36223, 7473, 842, 47, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The RG functions used here are defined by f(1)=1, f(j) <= 1+max_{i1. Conjecture: T(n+1,n-1) = 2+n*(n+1)*(3*n^2-5*n+26)/24 for n>1. Sum_{k=1..n} k * T(n,k) = A346772(n). - Alois P. Heinz, Aug 03 2021 EXAMPLE The two restricted growth functions of length 2 are (1,1) and (1,2). The 1 appears 3 times and the 2 once, so T(2,1)=3 and T(2,2)=1. 1; 3,1; 9,5,1; 30,21,8,1; 112,88,47,12,1; 463,387,253,97,17,1; 2095,1816,1345,675,184,23,1; 10279,9123,7304,4418,1641,324,30,1; 54267,48971,41193,28396,13276,3645,536,38,1; 306298,279855,243152,183615,102244,36223,7473,842,47,1; 1838320,1695902,1506521,1211936,770989,334751,90223,14303,1267,57,1; 11677867,10856879,9799547,8237223,5795889,2965654,995191,207186,25820, 1839,68,1; MAPLE b:= proc(n, m) option remember; `if`(n=0, [1, 0], add((p-> [p[1], p[2]+p[1]*x^j])(b(n-1, max(m, j))), j=1..m+1)) end: T:= n-> (p-> seq(coeff(p, x, i), i=1..n))(b(n, 0)[2]): seq(T(n), n=0..12); # Alois P. Heinz, Mar 14 2016 MATHEMATICA b[n_, m_] := b[n, m] = If[n == 0, {1, 0}, Sum[Function[p, {p[[1]], p[[2]] + p[[1]]*x^j}][b[n-1, Max[m, j]]], {j, 1, m+1}]]; T[n_] := Function[p, Table[Coefficient[p, x, i], {i, 1, n}]][b[n, 0][[2]] ]; Table[T[n], {n, 0, 12}] // Flatten (* Jean-François Alcover, Apr 07 2016, after Alois P. Heinz *) CROSSREFS Cf. A070071 (row sums). Column p=1-10 gives: A124427, A270494, A270495, A270496, A270497, A270498, A270499, A270500, A270501, A270502. T(2n+1,n+1) gives A270529. Cf. A000110, A185105, A285362, A286416, A346772. Sequence in context: A331257 A112626 A050155 * A140714 A112932 A337680 Adjacent sequences: A270233 A270234 A270235 * A270237 A270238 A270239 KEYWORD nonn,tabl AUTHOR R. J. Mathar, Mar 13 2016 STATUS approved

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

Last modified July 23 21:46 EDT 2024. Contains 374575 sequences. (Running on oeis4.)