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 A111212 Number of distinct integers d(pi), where pi ranges over all partitions of n into distinct parts and d(pi) = sum of squares of parts of pi. 2
 1, 1, 1, 2, 2, 3, 4, 5, 6, 7, 10, 12, 12, 18, 20, 23, 27, 35, 32, 46, 48, 55, 59, 79, 74, 94, 101, 110, 127, 144, 134, 172, 180, 189, 205, 235, 237, 266, 282, 303, 323, 352, 346, 391, 403, 436, 453, 497, 492, 547, 555, 596, 606, 661, 670, 724, 741, 775, 806, 861 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..500 (first 301 terms from Joerg Arndt) EXAMPLE The 8 partitions of 9 into distinct parts have these sums of squares: 81, 65, 53, 45, 41, 41, 35, 29, where 41 = 6^2 + 2^2 + 1^2 = 5^2 + 4^2, so that a(9) = 7. - Clark Kimberling, Apr 13 2014 MAPLE seq(`if`(m=2, 1, nops(simplify(coeff(series(mul(1+x^(k^2)*y^k, k=1..61), y, 61), y, m)))), m=0..60); # second Maple program: b:= proc(n, i) option remember; `if`(i*(i+1)/2x+i^2, b(n-i, min(n-i, i-1)))[]})) end: a:= n-> nops(b(n\$2)): seq(a(n), n=0..65); # Alois P. Heinz, Apr 18 2019 MATHEMATICA z = 40; g[n_] := n^2; q[n_] := q[n] = Select[IntegerPartitions[n], Max[Length /@ Split@#] == 1 &]; Map[Length, Map[Union, Table[Total[Map[g, q[n][[k]]]], {n, 1, z}, {k, 1, PartitionsQ[n]}]]] (* Clark Kimberling, Apr 13 2014 *) terms = 60; s = (Product[1+x^k^2*y^k, {k, terms}] + O[y]^terms) + O[x]^terms^2; Join[{1, 1}, Length /@ CoefficientList[s, y][[3 ;; terms]]] (* Jean-François Alcover, Jan 29 2018, adapted from Maple *) CROSSREFS Cf. A000009, A069999. Sequence in context: A301513 A066639 A370808 * A338317 A141286 A165686 Adjacent sequences: A111209 A111210 A111211 * A111213 A111214 A111215 KEYWORD easy,nonn AUTHOR Vladeta Jovovic, Oct 25 2005 EXTENSIONS Corrected term a(2), Joerg Arndt, Apr 18 2019 STATUS approved

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Last modified September 19 03:30 EDT 2024. Contains 376004 sequences. (Running on oeis4.)