A364842 Table read by antidiagonals: row n gives the Euler transform of the sequence (2,...,2,0,0,...) that contains n 2s followed by 0s.

1, 1, 2, 1, 2, 3, 1, 2, 5, 4, 1, 2, 5, 8, 5, 1, 2, 5, 10, 14, 6, 1, 2, 5, 10, 18, 20, 7, 1, 2, 5, 10, 20, 30, 30, 8, 1, 2, 5, 10, 20, 34, 49, 40, 9, 1, 2, 5, 10, 20, 36, 59, 74, 55, 10, 1, 2, 5, 10, 20, 36, 63, 94, 110, 70, 11, 1, 2, 5, 10, 20, 36, 65, 104, 149, 158, 91, 12

Offset

1,3

Links

Table of n, a(n) for n=1..78.

Example

Table begins:
  | 0 1 2  3  4  5  6   7   8   9  10
--+----------------------------------
1 | 1 2 3  4  5  6  7   8   9  10  11
2 | 1 2 5  8 14 20 30  40  55  70  91
3 | 1 2 5 10 18 30 49  74 110 158 221
4 | 1 2 5 10 20 34 59  94 149 224 334
5 | 1 2 5 10 20 36 63 104 169 264 405
6 | 1 2 5 10 20 36 65 108 179 284 445
7 | 1 2 5 10 20 36 65 110 183 294 465
8 | 1 2 5 10 20 36 65 110 185 298 475
9 | 1 2 5 10 20 36 65 110 185 300 479

Mathematica

Seed[i_, n_] := ConstantArray[2, i]~Join~ConstantArray[0, n - i];
A364842Table[n_] := Table[Seed[i, n] // EulerTransform, {i, 1, n}]
(*EulerTransform is defined in A005195*)

Crossrefs

Cf. A000027 (row 1), A006918 (row 2), A117485 (row 3), A117486 ( row 4), A117487 (row 5), A160647 (row 6), A000712 (main diagonal).

Analogous for initial 1s sequence A008284.

Cf. A115994.

Sequence in context: A134628 A064882 A065158 * A181842 A209564 A029653

Adjacent sequences: A364839 A364840 A364841 * A364843 A364844 A364845

Keyword

nonn,tabl

Author

Peter Kagey, Nov 09 2023

Status

approved