cp's OEIS Frontend

A182276 Sum of all parts minus the total number of parts of the shell model of partitions with n regions.

%I A182276 #27 Oct 16 2024 06:03:28
%S A182276 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 A182276 100,110,112,119,123,142,143,147,149,158,162,165,181,184,192,197,201,
%U A182276 228,230,235,238,248,250,257,261,280,284,287,299,305,310,341
%N A182276 Sum of all parts minus the total number of parts of the shell model of partitions with n regions.
%C A182276 For the definition of "region of n" see A206437.
%F A182276 a(n) = A182244(n) - A182181(n).
%F A182276 a(A000041(n)) = A196087(n).
%e A182276 Written has a triangle:
%e A182276 0,
%e A182276 1,
%e A182276 3,
%e A182276 4,    8;
%e A182276 10,  15;
%e A182276 16,  20, 22, 31;
%e A182276 33,  38, 41, 51;
%e A182276 52,  56, 58, 67, 71, 74, 90;
%e A182276 92,  97,100,110,112,119,123,142;
%e A182276 143,147,149,158,162,165,181,184,192,197,201,228;
%e A182276 230,235,238,248,250,257,261,280,284,287,299,305,310,341;
%t A182276 lex[n_]:=DeleteCases[Sort@PadRight[Reverse /@ IntegerPartitions@n], x_ /; x==0,2];
%t A182276 reg = {}; l = {};
%t A182276 For[j = 1, j <= 56, j++,
%t A182276   mx = Max@lex[j][[j]]; AppendTo[l, mx];
%t A182276   For[i = j, i > 0, i--, If[l[[i]] > mx, Break[]]];
%t A182276   t = Take[Reverse[First /@ lex[mx]], j - i];
%t A182276   AppendTo[reg, Total@t - Length@t]
%t A182276   ];
%t A182276 Accumulate@reg  (* _Robert Price_, Jul 25 2020 *)
%Y A182276 Row j has length A187219(j). Right border gives A196087.
%Y A182276 Cf. A000041, A066186, A006128, A135010, A138121, A182181, A182244, A186114, A206437, A207035.
%K A182276 nonn
%O A182276 1,3
%A A182276 _Omar E. Pol_, Apr 23 2012