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A096541
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Number of parts unequal to 1 in all partitions of the integer n. Also the difference between the labeled and the unlabeled case of one-element transitions from the partitions of n to the partitions of n+1.
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5
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0, 0, 1, 2, 5, 8, 16, 24, 41, 61, 95, 136, 204, 284, 407, 560, 779, 1050, 1432, 1901, 2543, 3338, 4393, 5698, 7411, 9513, 12226, 15562, 19803, 24993, 31538, 39506, 49456, 61546, 76499, 94603, 116858, 143679, 176431, 215802, 263576, 320796, 389900
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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FORMULA
| a(n) = A093694(n) - A000070(n).
a(n) = Sum_{k=1..n} (tau(k)-1)*numbpart(n-k). - Vladeta Jovovic (vladeta(AT)eunet.rs), Jun 26 2004
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EXAMPLE
| The partitions of n=5 are [11111], [1112], [113], [122], [23], [14], [5] and they contain 0 + 1 + 1 + 2 + 2 + 1 + 1 = 8 = A096541(5) parts unequal to 1.
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MAPLE
| main := proc(n::integer) local a, ndxp, ndxprt, ListOfPartitions, iverbose; with(combinat): ListOfPartitions:=partition(n); a:=0; for ndxp from 1 to nops(ListOfPartitions) do for ndxprt from 1 to nops(ListOfPartitions[ndxp]) do if op(ndxprt, ListOfPartitions[ndxp]) <> 1 then a := a + 1; fi; end do; end do; print("n, a(n):", n, a); end proc;
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MATHEMATICA
| first Needs["DiscreteMath`Combinatorica`"] then f[n_] := Block[{l = Sort[ Flatten[ Partitions[n]]]}, Length[l] - Count[l, 1]]; Table[ f[n], {n, 0, 20}] (Robert G. Wilson v)
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CROSSREFS
| Cf. A093694, A093695, A094533, A006128.
Sequence in context: A168470 A129299 A171238 * A137685 A169826 A093065
Adjacent sequences: A096538 A096539 A096540 * A096542 A096543 A096544
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KEYWORD
| nonn
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AUTHOR
| Thomas Wieder (wieder.thomas(AT)t-online.de), Jun 24 2004
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EXTENSIONS
| More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Jun 30 2004
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