A180039 Combinatorial tetrahedral numbers.
1, 112, 111223, 1111222334, 111112222333445, 111111222223333444556, 1111111222222333334444555667, 111111112222222333333444445555666778, 111111111222222223333333444444555556666777889
Offset: 1
Examples
For n=4, a(4)= 1 + 111 + 111111 + 1111111111 = 1111222334. Combinatorially: 1,12,123,1234,12345,123456,... 1,21,321,4321,54321,654321,... ----------------------------- X 1,112,111223,1111222334....... For n =(4),a(4)= 4 x 1 + 3 x 2 + 2 x 3 + 1 x 4 = 1111 + 222 + 33 + 4 = 1111222334.
Programs
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Mathematica
Accumulate[Table[FromDigits[PadRight[{},n,1]],{n,Accumulate[Range[10]]}]] (* Harvey P. Dale, Jun 12 2021 *)
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