A373301 - OEIS

A373301

Sum of successive nonnegative integers in a row of length p(n) where p counts integer partitions.

0, 3, 12, 40, 98, 253, 540, 1199, 2415, 4893, 9268, 17864, 32421, 59265, 104632, 184338, 315414, 540155, 901845, 1504173, 2461932, 4013511, 6443170, 10314675, 16281749, 25608450, 39838855, 61716941, 94682665, 144726102

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OFFSET

1,2

COMMENTS

The length of each row is given by A000041.

As many sequences start like the nonnegative integers, their row sums when disposed in this shape start with the same values.

Here is a sample list by A-number order of the sequences which are sufficiently close to A001477 to have the same row sums for at least 8 terms: A089867, A089868, A089869, A089870, A118760, A123719, A130696, A136602, A254109, A258069, A258070, A258071, A266279, A272813, A273885, A273886, A273887, A273888.

LINKS

Table of n, a(n) for n=1..30.

EXAMPLE

Illustration of the first few terms

0 | 0

3 | 1, 2

12 | 3, 4, 5

40 | 6, 7, 8, 9, 10

98 | 11, 12, 13, 14, 15, 16, 17

253 | 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28

540 | 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43

MATHEMATICA

Module[{s = -1},

Table[s +=

PartitionsP[

n - 1]; (s + PartitionsP[n]) (s + PartitionsP[n] - 1)/2 -

s (s - 1)/2, {n, 1, 30}]]

CROSSREFS

Cf. A373300, original version, with positive integers A000027.

Cf. A001477, the nonnegative integers.

Cf. A027480, the sequence of row sums for a regular triangle.

Sequence in context: A303348 A237036 A034956 * A032093 A007993 A293366

Adjacent sequences: A373298 A373299 A373300 * A373302 A373303 A373304

KEYWORD

nonn

AUTHOR

Olivier Gérard, May 31 2024

STATUS

approved