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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).
0
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
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).
Mini-index to these sequences: A064766, A064865, A064866, A065221-A655234 are all of the same type. See A064766 for a detailed explanation.
Sequence in context: A004157 A331514 A091068 * A345681 A243658 A072452
KEYWORD
easy,nonn
AUTHOR
Floor van Lamoen, Oct 22 2001
EXTENSIONS
Edited by N. J. A. Sloane, Jun 03 2020
STATUS
approved