A210763 - OEIS

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A210763

Tetrahedron T(j,n,k) in which the slice j is a finite triangle read by rows T(n,k) which lists the sums of the columns of the shell model of partitions with n shells.

1, 1, 1, 2, 1, 1, 2, 1, 1, 3, 1, 1, 2, 2, 2, 3, 1, 1, 2, 5, 1, 1, 2, 2, 2, 3, 2, 2, 3, 5, 1, 1, 1, 2, 7, 1, 1, 2, 2, 2, 3, 3, 3, 3, 5, 3, 3, 4, 4, 7, 1, 1, 1, 2, 4, 11, 1, 1, 2, 2, 2, 3, 3, 3, 3, 5, 4, 4, 5, 4, 7, 3, 3, 3, 5, 6, 11, 1, 1, 1, 1, 2, 4, 15

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

OFFSET

1,4

LINKS

Table of n, a(n) for n=1..84.

EXAMPLE

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Illustration of first five A210952

slices of the tetrahedron Row sum

--------------------------------------------------------

. 1, 1

. 1, 2, 3

. 1, 1

. 1, 2, 3

. 1, 1, 3, 5

. 1, 1

. 1, 2, 3

. 2, 2, 3, 7

. 1, 1, 2, 5, 9

. 1, 1

. 1, 2, 3

. 2, 2, 3, 7

. 2, 2, 3, 5, 12

. 1, 1, 1, 2, 7, 12

--------------------------------------------------------

. 1, 2, 2, 3, 3, 3, 5, 5, 5, 5, 7, 7, 7, 7, 7,

Each column sum in the slice j is equal to A000041(j).

Also this sequence can be written as a triangle read by rows in which each row is a flattened triangle. The sequence begins:

1,1,2;

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

1,1,2,2,2,3,1,1,2,5;

1,1,2,2,2,3,2,2,3,5,1,1,1,2,7;

1,1,2,2,2,3,3,3,3,5,3,3,4,4,7,1,1,1,2,4,11;

1,1,2,2,2,3,3,3,3,5,4,4,5,4,7,3,3,3,5,6,11,1,1,1,1,2,4,15;

Row n has length A000217(n). Row sums give A066186. Right border gives A000041(n), n >= 1.

CROSSREFS

Cf. A135010, A138121, A209655, A209918, A210952, A210960, A210961.

Sequence in context: A343407 A359236 A320010 * A281681 A218799 A078770

Adjacent sequences: A210760 A210761 A210762 * A210764 A210765 A210766

KEYWORD

nonn,tabf

AUTHOR

Omar E. Pol, Apr 24 2012

STATUS

approved