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 A213679 Total sum of parts <= n of multiplicity 0 in all partitions of n. 2
 0, 0, 3, 11, 36, 79, 186, 345, 672, 1163, 2026, 3273, 5388, 8301, 12912, 19349, 28961, 42071, 61253, 86921, 123404, 171972, 239020, 327386, 447743, 604255, 813645, 1084657, 1441643, 1899450, 2496510, 3255653, 4234822, 5472953, 7053217, 9038784, 11554020 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..1000 FORMULA a(n) = A000217(n)*A000041(n)-A014153(n-1). EXAMPLE The partitions of n=4 are [1,1,1,1], [2,1,1], [2,2], [3,1], [4]. Parts <= 4 with multiplicity m=0 sum up to (2+3+4)+(3+4)+(1+3+4)+(2+4)+(1+2+3) = 36, thus a(4) = 36. MAPLE b:= proc(n, p) option remember; `if`(n=0 and p=0, [1, 0], `if`(p<1, [0\$2], add((l->`if`(m=0, l+[0, l[1]*p], l))(b(n-p*m, p-1)), m=0..n/p))) end: a:= n-> b(n, n)[2]: seq(a(n), n=0..55); MATHEMATICA b[n_, p_] := b[n, p] = If[n == 0 && p == 0, {1, 0}, If[p == 0, Array[0&, n+2], Sum[Function[l, ReplacePart[l, m+2 -> p*l[[1]] + l[[m+2]]]][Join[b[n-p*m, p-1], Array[0&, p*m]]], {m, 0, n/p}]]]; a[n_] := b[n, n][[2]]; Table[a[n], {n, 0, 55}] (* Jean-François Alcover, Jan 24 2014, after Alois P. Heinz *) CROSSREFS Column k=0 of A222730. Cf. A000041, A000217, A014153. Sequence in context: A119143 A119092 A119177 * A297577 A119126 A119088 Adjacent sequences: A213676 A213677 A213678 * A213680 A213681 A213682 KEYWORD nonn AUTHOR Alois P. Heinz, Mar 04 2013 STATUS approved

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Last modified September 23 09:36 EDT 2023. Contains 365544 sequences. (Running on oeis4.)