A210966 Sum of all region numbers of all parts of the n-th region of the shell model of partitions.

1, 4, 9, 4, 25, 6, 49, 8, 18, 10, 121, 12, 26, 14, 225, 16, 34, 18, 76, 20, 21, 484, 23, 48, 25, 104, 27, 56, 29, 900, 31, 64, 33, 136, 35, 36, 259, 38, 78, 40, 41, 1764, 43, 88, 45, 184, 47, 96, 49, 400, 51, 52, 159, 54, 55, 3136, 57, 116, 59, 240

Offset

1,2

Comments

Each part of a partition of n belongs to a different region of n. The "region number" of a part of the r-th region of n is equal to r. For the definition of "region of n" see A206437.

Links

Table of n, a(n) for n=1..60.

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

Formula

a(n) = n*A194446(n).

Example

The first seven regions of the shell model of partitions (or the seven regions of 5) are [1], [2, 1], [3, 1, 1], [2], [4, 2, 1, 1, 1], [3], [5, 2, 1, 1, 1, 1, 1] therefore the "region numbers" are [1], [2, 2], [3, 3, 3], [4], [5, 5, 5, 5, 5], [6], [7, 7, 7, 7, 7, 7, 7]. So a(1)..a(7) give: 1, 4, 9, 4, 25, 6, 49.
Also written as an irregular triangle the sequence begins:
1;
4;
9;
4,25;
6,49;
8,18,10,121;
12,26,14,225;
16,34,18,76,20,21,484;
23,48,25,104,27,56,29,900;
31,64,33,136,35,36,259,38,78,40,41,1764;
43,88,45,184,47,96,49,400,51,52,159,54,55,3136;

Crossrefs

Row n has length A187219(n). Row sums give A210969. Right border gives A001255, n >= 1.

Cf. A135010, A138121, A194446, A182703, A206437, A210971, A210972.

Sequence in context: A088377 A066048 A103164 * A300516 A178147 A005063

Adjacent sequences: A210963 A210964 A210965 * A210967 A210968 A210969

Keyword

nonn,tabf

Author

Omar E. Pol, Jul 01 2012

Status

approved