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%I #24 Jul 25 2020 13:02:58
%S 0,1,3,4,8,10,15,16,20,22,31,33,38,41,51,52,56,58,67,71,74,90,92,97,
%T 100,110,112,119,123,142,143,147,149,158,162,165,181,184,192,197,201,
%U 228,230,235,238,248,250,257,261,280,284,287,299,305,310,341
%N Sum of all parts minus the total number of parts of the shell model of partitions with n regions.
%C For the definition of "region of n" see A206437.
%F a(n) = A182244(n) - A182181(n).
%F a(A000041(n) = A196087(n).
%e Written has a triangle:
%e 0,
%e 1,
%e 3,
%e 4, 8;
%e 10, 15;
%e 16, 20, 22, 31;
%e 33, 38, 41, 51;
%e 52, 56, 58, 67, 71, 74, 90;
%e 92, 97,100,110,112,119,123,142;
%e 143,147,149,158,162,165,181,184,192,197,201,228;
%e 230,235,238,248,250,257,261,280,284,287,299,305,310,341;
%t lex[n_]:=DeleteCases[Sort@PadRight[Reverse /@ IntegerPartitions@n], x_ /; x==0,2];
%t reg = {}; l = {};
%t For[j = 1, j <= 56, j++,
%t mx = Max@lex[j][[j]]; AppendTo[l, mx];
%t For[i = j, i > 0, i--, If[l[[i]] > mx, Break[]]];
%t t = Take[Reverse[First /@ lex[mx]], j - i];
%t AppendTo[reg, Total@t - Length@t]
%t ];
%t Accumulate@reg (* _Robert Price_, Jul 25 2020 *)
%Y Row j has length A187219(j). Right border gives A196087.
%Y Cf. A000041, A066186, A006128, A135010, A138121, A182181, A182244, A186114, A206437, A207035.
%K nonn
%O 1,3
%A _Omar E. Pol_, Apr 23 2012
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