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.

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, 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, 2, 2, 2, 3, 3, 2, 2, 6, 2, 2, 5, 3, 2, 4, 4, 2, 8, 2

Offset

1,2

Comments

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).

Row n lists the largest part and the parts > 1 of the n-th zone of the model.

Links

Table of n, a(n) for n=1..86.

Omar E. Pol, Illustration of the partitions and regions of n, for n = 1..12

Mikhail Kurkov, PARI program. [verification needed]

Example

Triangle                First 15 zones of the
begins                  shell model of partitions
--------------------------------------------------
1;                      1 1 1 1 1 1 1 1 1 1 1...
2;                      . 2 1 1 1 1 1 1 1 1 1...
3;                      . . 3 1 1 1 1 1 1 1 1...
2, 2;                   . 2 . 2 1 1 1 1 1 1 1...
4;                      . . . 4 1 1 1 1 1 1 1...
3, 2;                   . . 3 . 2 1 1 1 1 1 1...
5;                      . . . . 5 1 1 1 1 1 1...
2, 2, 2;                . 2 . 2 . 2 1 1 1 1 1...
4, 2;                   . . . 4 . 2 1 1 1 1 1...
3, 3;                   . . 3 . . 3 1 1 1 1 1...
6;                      . . . . . 6 1 1 1 1 1...
3, 2, 2;                . . 3 . 2 . 2 1 1 1 1...
5, 2;                   . . . . 5 . 2 1 1 1 1...
4, 3;                   . . . 4 . . 3 1 1 1 1...
7;                      . . . . . . 7 1 1 1 1...

Prog

(PARI)
a210941(n)={
    my(p=[], r=[1]);
    if(n>1,
    my(c=2);
    while(#r<n,
        p=vecsort(partitions(c));
        r=concat(r, concat([Vecrev(x) | x<-p, x[1]<>1]));
        c++));
    return(r[1..n])
} \\ Joe Slater, Sep 02 2024

Crossrefs

Column 1 is A141285. Row n has length A194548(n), n > 1.

Cf. A135010, A138121, A182703, A194711, A206437, A210942, A210943.

Sequence in context: A241019 A023581 A023574 * A193827 A131340 A337121

Adjacent sequences: A210938 A210939 A210940 * A210942 A210943 A210944

Keyword

nonn,tabf

Author

Omar E. Pol, Apr 18 2012

Status

approved