A194449 - OEIS

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A194449

Largest part minus the number of parts > 1 in the n-th region of the set of partitions of j, if 1 <= n <= A000041(j).

1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 2, 2, 3, 3, 3, 1, 2, 2, 2, 4, 3, 1, 2, 3, 3, 3, 2, 4, 4, 1, 1, 2, 2, 2, 4, 3, 1, 3, 5, 5, 4, -2, 2, 3, 3, 3, 2, 4, 4, 1, 4, 3, 5, 6, 5, -3, 1, 2, 2, 2, 4, 3, 1, 3, 5, 5, 4, -2, 2, 4, 4, 5, 3, 6, 6, 5, -9

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,3

COMMENTS

Also triangle read by rows: T(j,k) = largest part minus the numbers of parts > 1 in the k-th region of the last section of the set of partitions of j. It appears that the sum of row j is equal to A000041(j-1). For the definition of "region" of the set of partitions of j see A206437. See also A135010.

LINKS

Table of n, a(n) for n=1..77.

Omar E. Pol, Illustration of the seven regions of 5

FORMULA

a(n) = A141285(n) - A194448(n).

EXAMPLE

The 7th region of the shell model of partitions is [5, 2, 1, 1, 1, 1, 1]. The largest part is 5 and the number of parts > 1 is 2, so a(7) = 5 - 2 = 3 (see an illustration in the link section).

Written as an irregular triangle T(j,k) begins:

1,2;

2,3;

1,2,2,2;

2,3,3,3;

1,2,2,2,4,3,1;

2,3,3,3,2,4,4,1;

1,2,2,2,4,3,1,3,5,5,4,-2;

2,3,3,3,2,4,4,1,4,3,5,6,5,-3;

1,2,2,2,4,3,1,3,5,5,4,-2,2,4,4,5,3,6,6,5,-9;

CROSSREFS

Row j has length A187219(j).

Cf. A000041, A135010, A138121, A138137, A138879, A186114, A186412, A193870, A194436, A194437, A194438, A194439, A194446, A194447, A206437.

Sequence in context: A354907 A086342 A274036 * A370820 A261923 A124736

Adjacent sequences: A194446 A194447 A194448 * A194450 A194451 A194452

KEYWORD

sign,tabf

AUTHOR

Omar E. Pol, Dec 10 2011

STATUS

approved