A065233 Fill a triangular array by rows by writing numbers 1 up to b(0), 1 up to b(1), etc., where the b(n) are the nonzero 9-gonal (nonagonal) numbers 1, 9, 24, 46, ... (A001106). The initial elements of the rows form a(n).

1, 1, 3, 6, 1, 6, 12, 19, 3, 12, 22, 33, 45, 12, 26, 41, 57, 74, 17, 36, 56, 77, 99, 11, 35, 60, 86, 113, 141, 16, 46, 77, 109, 142, 176, 7, 43, 80, 118, 157, 197, 238, 19, 62, 106, 151, 197, 244, 292, 16, 66, 117, 169, 222, 276, 331, 387, 48, 106, 165, 225, 286, 348

Offset

0,3

Links

Table of n, a(n) for n=0..62.

Example

The triangle begins as follows (the slashes indicate the numbers b(0), b(1), b(2), ...):
1/
1 2
3 4 5
6 7 8 9/
1 2 3 4 5
6 7 8 9 10 11
12 13 14 15 16 17 18
19 20 21 22 23 24/ 1 2
3 4 ...
The initial terms in the rows give the sequence 1, 1, 3, 6, 1, 6, ...

Mathematica

Module[{nn=20, p9}, p9=Flatten[Range[#]&/@PolygonalNumber[9, Range[nn]]]; TakeList[p9, Range[Floor[(Sqrt[1+8Length[p9]]-1)/2]]]][[All, 1]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jun 04 2020 *)

Crossrefs

Cf. A064766 (based on the triangular numbers), A064865 (the squares), A065221-A065232, A065234.

Sequence in context: A004157 A331514 A091068 * A345681 A243658 A072452

Adjacent sequences: A065230 A065231 A065232 * A065234 A065235 A065236

Keyword

easy,nonn

Author

Floor van Lamoen, Oct 22 2001

Extensions

Edited by N. J. A. Sloane, Jun 03 2020

Status

approved