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%I #19 Apr 06 2023 10:19:25
%S 0,1,3,6,15,28,36,45,55,66,78,136,378,666,1128,1225,1378,2278,2346,
%T 2556,5778,12246,13366,22366,22578,35778,111156,222778,223446,333336,
%U 1113778,1222266,1457778,2235555,3557778,22227778,22234446,111116778,156777778,222446778
%N Triangular numbers with digits in nondecreasing order.
%C Beyond 222446778, all terms are k(k+1)/2 for k = 2s7, 6s7, or 6s8, where s stands for any number of 6's. - _T. D. Noe_, Jan 01 2014
%H T. D. Noe, <a href="/A234848/b234848.txt">Table of n, a(n) for n = 1..328</a> (terms less than 10^200)
%t inOrder[nums_] := Min[Differences[nums]] >= 0; t = {}; Do[tri = n*(n+1)/2; If[inOrder[IntegerDigits[tri]], AppendTo[t, tri]], {n, 0, 10^5}]; t (* _T. D. Noe_, Dec 31 2013 *)
%t Select[Accumulate[Range[0,22000]],Min[Differences[IntegerDigits[#]]]>=0&] (* _Harvey P. Dale_, Apr 06 2023 *)
%o (Python)
%o from itertools import chain, count, islice, combinations_with_replacement
%o from sympy import integer_nthroot
%o def A234848_gen(): # generator of terms
%o return chain((0,), (n for n in (int(''.join(i)) for l in count(1) for i in combinations_with_replacement('123456789',l)) if integer_nthroot(8*n+1,2)[1]))
%o A234848_list = list(islice(A234848_gen(),50)) # _Chai Wah Wu_, May 22 2022
%Y Cf. A000217, A028820.
%K base,nonn
%O 1,3
%A _Zak Seidov_, Dec 31 2013
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