cp's OEIS Frontend

A210941 Triangle read by rows in which row n lists the parts > 1 of the n-th zone of the shell model of partitions, with a(1) = 1.

%I A210941 #43 Oct 10 2024 16:01:39
%S A210941 1,2,3,2,2,4,3,2,5,2,2,2,4,2,3,3,6,3,2,2,5,2,4,3,7,2,2,2,2,4,2,2,3,3,
%T A210941 2,6,2,5,3,4,4,8,3,2,2,2,5,2,2,4,3,2,7,2,3,3,3,6,3,5,4,9,2,2,2,2,2,4,
%U A210941 2,2,2,3,3,2,2,6,2,2,5,3,2,4,4,2,8,2
%N A210941 Triangle read by rows in which row n lists the parts > 1 of the n-th zone of the shell model of partitions, with a(1) = 1.
%C A210941 The n-th zone of the shell model of partitions is formed by the parts of row n followed by infinitely many parts of size 1 (see example and also A210943).
%C A210941 Row n lists the largest part and the parts > 1 of the n-th zone of the model.
%H A210941 Omar E. Pol, <a href="http://www.polprimos.com/imagenespub/polpa308.jpg">Illustration of the partitions and regions of n, for n = 1..12</a>
%H A210941 Mikhail Kurkov, <a href="/A210941/a210941.txt">PARI program</a>. [verification needed]
%e A210941 Triangle                First 15 zones of the
%e A210941 begins                  shell model of partitions
%e A210941 --------------------------------------------------
%e A210941 1;                      1 1 1 1 1 1 1 1 1 1 1...
%e A210941 2;                      . 2 1 1 1 1 1 1 1 1 1...
%e A210941 3;                      . . 3 1 1 1 1 1 1 1 1...
%e A210941 2, 2;                   . 2 . 2 1 1 1 1 1 1 1...
%e A210941 4;                      . . . 4 1 1 1 1 1 1 1...
%e A210941 3, 2;                   . . 3 . 2 1 1 1 1 1 1...
%e A210941 5;                      . . . . 5 1 1 1 1 1 1...
%e A210941 2, 2, 2;                . 2 . 2 . 2 1 1 1 1 1...
%e A210941 4, 2;                   . . . 4 . 2 1 1 1 1 1...
%e A210941 3, 3;                   . . 3 . . 3 1 1 1 1 1...
%e A210941 6;                      . . . . . 6 1 1 1 1 1...
%e A210941 3, 2, 2;                . . 3 . 2 . 2 1 1 1 1...
%e A210941 5, 2;                   . . . . 5 . 2 1 1 1 1...
%e A210941 4, 3;                   . . . 4 . . 3 1 1 1 1...
%e A210941 7;                      . . . . . . 7 1 1 1 1...
%o A210941 (PARI)
%o A210941 a210941(n)={
%o A210941     my(p=[],r=[1]);
%o A210941     if(n>1,
%o A210941     my(c=2);
%o A210941     while(#r<n,
%o A210941         p=vecsort(partitions(c));
%o A210941         r=concat(r,concat([Vecrev(x) | x<-p,x[1]<>1]));
%o A210941         c++));
%o A210941     return(r[1..n])
%o A210941 } \\ _Joe Slater_, Sep 02 2024
%Y A210941 Column 1 is A141285. Row n has length A194548(n), n > 1.
%Y A210941 Cf. A135010, A138121, A182703, A194711, A206437, A210942, A210943.
%K A210941 nonn,tabf
%O A210941 1,2
%A A210941 _Omar E. Pol_, Apr 18 2012