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%I #15 Mar 12 2023 08:48:38
%S 1,112,11223,1122334,112233445,11223344556,1122334455667,
%T 112233445566778,11223344556677889,1122334455667789000,
%U 112233445566778900111,11223344556677890011222,1122334455667789001122333,112233445566778900112233444,11223344556677890011223344555,1122334455667789001122334455666
%N Partial sums of A100706.
%C Up to n=8 the digits of a(n) sum up to n^2.
%C Similar to this, A014824 (1,12,123,1234,...) is a representation of the triangular numbers; (1,1112,1112223,1112223334,...) of the pentagonal numbers;(1,11112,111122223,...) of the hexagonal numbers, and so on. A nice thing about this sequence(s) is that the (represented) value of the integer matches the partial sums of the number of digits in the sequence.
%C f(n) = 100*f(n-1) + A100706(n) gives a mirrored version of this sequence, and f(n) = 10*f(n-1) + A100706(n) the symmetrical version (A002477).
%F a(n) = Sum_{k=0..n} A100706(k). - _Michel Marcus_, Mar 12 2023
%o (PARI) A100706(n) = (10^(2*n + 1) - 1)/9;
%o a(n) = sum(k=0, n, A100706(k)); \\ _Michel Marcus_, Mar 12 2023
%Y Cf. A014824, A100706, A002477.
%K nonn
%O 0,2
%A _Mark Dols_, Aug 07 2010
%E More terms and edited by _Michel Marcus_, Mar 12 2023
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