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%I #8 Jun 12 2021 12:51:58
%S 1,112,111223,1111222334,111112222333445,111111222223333444556,
%T 1111111222222333334444555667,111111112222222333333444445555666778,
%U 111111111222222223333333444444555556666777889
%N Combinatorial tetrahedral numbers
%C These are partial sums in adding base-1 triangular numbers (1 + 111 + 111111 + 1111111111,...).
%C Third row of:
%C 1,2,3,4,5,...
%C 1,12,123,1234,12345,...
%C 1,112,111223,1111222334,111112222333445,...
%C 1,1112,1111112223,11111111112222223334,11111111111111122222222223333334445,..
%F a(n) = Sum_{i=1..n} A002275(A000217(i)). - _R. J. Mathar_, Nov 02 2016
%e For n=4, a(4)= 1 + 111 + 111111 + 1111111111 = 1111222334.
%e Combinatorially:
%e 1,12,123,1234,12345,123456,...
%e 1,21,321,4321,54321,654321,...
%e ----------------------------- X
%e 1,112,111223,1111222334.......
%e For n =(4),a(4)= 4 x 1 + 3 x 2 + 2 x 3 + 1 x 4 = 1111 + 222 + 33 + 4 = 1111222334.
%t Accumulate[Table[FromDigits[PadRight[{},n,1]],{n,Accumulate[Range[10]]}]] (* _Harvey P. Dale_, Jun 12 2021 *)
%Y Cf. A000292, A014824, A180027.
%K nonn,easy,base
%O 1,2
%A _Mark Dols_, Aug 07 2010