%I #16 Nov 01 2024 15:06:04
%S 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,
%T 60,86,113,141,16,46,77,109,142,176,7,43,80,118,157,197,238,19,62,106,
%U 151,197,244,292,16,66,117,169,222,276,331,387,48,106,165,225,286,348
%N 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).
%e The triangle begins as follows (the slashes indicate the numbers b(0), b(1), b(2), ...):
%e 1/
%e 1 2
%e 3 4 5
%e 6 7 8 9/
%e 1 2 3 4 5
%e 6 7 8 9 10 11
%e 12 13 14 15 16 17 18
%e 19 20 21 22 23 24/ 1 2
%e 3 4 ...
%e The initial terms in the rows give the sequence 1, 1, 3, 6, 1, 6, ...
%t 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 *)
%Y Cf. A064766 (based on the triangular numbers), A064865 (the squares).
%Y Mini-index to these sequences: A064766, A064865, A064866, A065221-A655234 are all of the same type. See A064766 for a detailed explanation.
%K easy,nonn
%O 0,3
%A _Floor van Lamoen_, Oct 22 2001
%E Edited by _N. J. A. Sloane_, Jun 03 2020