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 A274046 a(n) is the smallest positive integer which can be represented as the sum of distinct positive triangular numbers in exactly n ways, or 0 if no such integer exists. 1
 1, 10, 25, 31, 49, 46, 55, 67, 70, 76, 82, 117, 102, 91, 97, 107, 101, 135, 110, 112, 116, 115, 119, 128, 0, 131, 133, 130, 148, 145, 136, 0, 137, 149, 154, 146, 0, 169, 152, 157, 155, 168, 171, 158, 174, 161, 0, 183, 184, 167, 0, 0, 173, 0, 175, 181, 190 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS 46 is the smallest number that can be expressed as the sum of distinct triangular numbers in five ways, but 49 is the smallest that can be so expressed in _exactly_ five ways. There are further examples of this phenomenon. LINKS EXAMPLE 25 = 1 + 3 + 6 + 15 = 10 + 15 = 1 + 3 + 21. This is the smallest number that can be written as the sum of distinct triangular numbers in three different ways. So a(3)=25. The first null values of a(n) occur for n = 25, 32, 37, 47, 51, 52, 54, 61,... - Giovanni Resta, Jun 08 2016 MATHEMATICA nT[n_, m_: 0] := nT[n, m] = If[n == 0, 1, Block[{t, i=m+1, s=0}, While[(t = i*(i+1)/2) <= n, s += nT[n-t, i]; i++]; s]]; a[n_] := Block[{k=0, t}, While[(t = nT[++k]) != n && t < Max[2*n, 30]]; If[t == n, k, 0]]; Array[a, 57] (* Giovanni Resta, Jun 08 2016 *) CROSSREFS Cf. A007294, A060773, A024940, A064816. Sequence in context: A133634 A174051 A225974 * A014090 A154057 A074814 Adjacent sequences:  A274043 A274044 A274045 * A274047 A274048 A274049 KEYWORD nonn AUTHOR Phil Scovis, Jun 07 2016 EXTENSIONS a(15)-a(20) from Tom Edgar, Jun 08 2016 a(21)-a(57) from Giovanni Resta, Jun 08 2016 STATUS approved

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Last modified November 26 09:38 EST 2020. Contains 338639 sequences. (Running on oeis4.)