A258069 -id:A258069 - cp's OEIS frontend

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

Offset: 1

Olivier Gérard, May 31 2024

nonn

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.

			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
.

Cf. A373300, original version, with positive integers A000027.
Cf. A001477, the nonnegative integers.
Cf. A027480, the sequence of row sums for a regular triangle.

Module[{s = -1},
 Table[s +=
   PartitionsP[
    n - 1]; (s + PartitionsP[n]) (s + PartitionsP[n] - 1)/2 -
   s (s - 1)/2, {n, 1, 30}]]

A321996 Numbers that cannot be written using six 6's and operations +, -, * and/or /. Complement of A171829.

Original entry on oeis.org

22, 26, 46, 50, 51, 52, 53, 55, 56, 57, 58, 59, 61, 62, 63, 64, 68, 76, 80, 81, 82, 83, 85, 86, 87, 88, 89, 91, 92, 93, 94, 95, 97, 98, 99, 100, 101, 103, 104, 105, 106, 110, 111, 112, 113, 115, 116, 117, 118, 119, 121, 122, 123, 124, 125, 127, 128, 129, 130, 131, 133, 134

Offset: 1

M. F. Hasler, Nov 23 2018

nonn

A171829 contains all but 3 nonnegative integers below 50, which motivates to list the complement, even though A171829 is finite and its complement, this sequence, contains all integers above 9072 except for 15552 and 46656. (These are the last three terms of A171829.)

Cf. A171829 (complement), A171826, A171827, A171828, A258068, A258069, A258070, A258071 (analog for 3, ..., 10).

Cf. A182002, A258097.

A321997 Numbers that cannot be written using seven 7's and operations +, -, * and/or /. Complement of A258068.

Original entry on oeis.org

38, 66, 67, 68, 73, 74, 75, 76, 79, 80, 81, 87, 88, 108, 109, 115, 116, 117, 118, 121, 122, 123, 124, 125, 127, 128, 129, 130, 131, 132, 134, 135, 136, 137, 138, 142, 143, 151, 152, 156, 157, 158, 159, 160, 162, 163, 164, 165, 166, 167, 169, 170, 173, 174, 176, 177, 178, 179

Offset: 1

M. F. Hasler, Nov 23 2018

nonn

A258068 contains most nonnegative integers below 115, which motivates listing the complement, even though A258068 is finite and its complement, this sequence, contains all integers above 134456 except for 235298 and 823543. (These are the last three terms of A258068.)

Cf. A258068 (complement), A171826, A171827, A171828, A171829, A258069, A258070, A258071 (analog for 3, ..., 10).

Cf. A182002, A258097.

cp's OEIS Frontend

A373301 Sum of successive nonnegative integers in a row of length p(n) where p counts integer partitions.

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A321996 Numbers that cannot be written using six 6's and operations +, -, * and/or /. Complement of A171829.

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A321997 Numbers that cannot be written using seven 7's and operations +, -, * and/or /. Complement of A258068.

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