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

Author

Floor van Lamoen, Oct 22 2001

Keywords

• easy
• nonn

Examples

			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, ...
		

Crossrefs

Cf. A064766 (based on the triangular numbers), A064865 (the squares).

Mini-index to these sequences: A064766, A064865, A064866, A065221-A655234 are all of the same type. See A064766 for a detailed explanation.

Programs

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 *)

Extensions

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