[seqfan] Re: a(n) = a(n-1) + [sum of all digits present so far]

[Jonathan Post]

so the array begins (done by hand, needs checking)

a(1) = k; a(n) = a(n-1) + sum of all decimal digits so far in the
sequence (row of array)

......|.n=1.|.n=2.|.n=3.|.n=4.|.n=5.|.n=6.|.n=7.|
k=1.|....1.|.....2.|.....5.|...13.|...25.|...44...|.71.|
k=2.|....2.|.....4.|.....8.|...16.|...39.|...90...|189.|
k=3.|....3.|.....6.|...21.|...45.|...99.|..216...|441.|

and main diagonal 1, 4, 21, ...?

I'd feel better if this were coded by someone...  But the idea of the
array is still, I think, valid, and gets beyond the arbitrariness of
starting with any given single a(1).

-- Jonathan Vos Post