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

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A213177 Number T(n,k) of parts in all partitions of n with largest multiplicity k; triangle T(n,k), n>=0, 0<=k<=n, read by rows. 14
 0, 0, 1, 0, 1, 2, 0, 3, 0, 3, 0, 3, 5, 0, 4, 0, 5, 6, 4, 0, 5, 0, 8, 9, 7, 5, 0, 6, 0, 10, 13, 13, 5, 6, 0, 7, 0, 13, 23, 14, 15, 6, 7, 0, 8, 0, 18, 30, 27, 16, 13, 7, 8, 0, 9, 0, 25, 44, 33, 30, 18, 15, 8, 9, 0, 10, 0, 30, 58, 55, 36, 34, 15, 17, 9, 10, 0, 11 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 LINKS Alois P. Heinz, Rows n = 0..140, flattened FORMULA T(n,k) = A210485(n,k) - A210485(n,k-1) for k>0, T(n,0) = 0. EXAMPLE T(6,1) = 8: partitions of 6 with largest multiplicity 1 are [3,2,1], [4,2], [5,1], [6], with 3+2+2+1 = 8 parts. T(6,2) = 9: [2,2,1,1], [3,3], [4,1,1]. T(6,3) = 7: [2,2,2], [3,1,1,1]. T(6,4) = 5: [2,1,1,1,1]. T(6,5) = 0. T(6,6) = 6: [1,1,1,1,1,1]. Triangle begins: 0; 0, 1; 0, 1, 2; 0, 3, 0, 3; 0, 3, 5, 0, 4; 0, 5, 6, 4, 0, 5; 0, 8, 9, 7, 5, 0, 6; 0, 10, 13, 13, 5, 6, 0, 7; 0, 13, 23, 14, 15, 6, 7, 0, 8; ... MAPLE b:= proc(n, i, k) option remember; `if`(n=0, [1, 0], `if`(i<1, [0, 0], add((l->[l[1], l[2]+l[1]*j])(b(n-i*j, i-1, k)), j=0..min(n/i, k)))) end: T:= (n, k)-> b(n, n, k)[2] -b(n, n, k-1)[2]: seq(seq(T(n, k), k=0..n), n=0..12); MATHEMATICA b[n_, i_, k_] := b[n, i, k] = If[n == 0, {1, 0}, If[i < 1, {0, 0}, Sum[b[n-i*j, i-1, k] /. l_List :> {l[[1]], l[[2]] + l[[1]]*j}, {j, 0, Min[n/i, k]}]]]; T[_, 0] = 0; T[n_, k_] := b[n, n, k][[2]] - b[n, n, k-1][[2]]; Table[Table[T[n, k], {k, 0, n}], {n, 0, 12}] // Flatten (* Jean-François Alcover, Dec 27 2013, translated from Maple *) CROSSREFS Columns k=0-10 give: A000004, A015723, A320372, A320373, A320374, A320375, A320376, A320377, A320378, A320379, A320380. Row sums give: A006128. Main diagonal and first lower diagonal give: A001477, A063524. T(2n,n) gives A320381. Cf. A091602, A210485. Sequence in context: A214000 A161123 A035442 * A265017 A349136 A035376 Adjacent sequences: A213174 A213175 A213176 * A213178 A213179 A213180 KEYWORD nonn,tabl AUTHOR Alois P. Heinz, Feb 27 2013 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 April 21 10:39 EDT 2024. Contains 371852 sequences. (Running on oeis4.)