A339379 - OEIS

%I #13 Jun 18 2022 10:04:00

%S 1,1,1,1,2,1,1,3,3,1,1,4,6,4,1,1,5,1,0,1,0,5,1,1,6,6,1,1,1,5,6,1,1,7,

%T 1,2,7,2,2,6,1,1,7,1,1,8,8,3,9,9,4,8,7,2,8,8,1,1,9,1,6,1,1,1,2,1,8,1,

%U 3,1,2,1,5,9,1,0,1,6,9,1

%N Irregular triangle read by rows; the first row simply contains the value 1; given the succession of digits of the n-th row, say [d_0, ..., d_k], the (n+1)-th row is the succession of digits of [d_0, d_0+d_1, d_1+d_2, ..., d_{k-1}+d_k, d_k].

%C This sequence combines features of Pascal's triangle (A007318) and of A093086.

%C Rows 0 to 4 match that of Pascal's triangle, thereafter the values differ.

%C Every column is eventually periodic.

%H Alois P. Heinz, <a href="/A339379/b339379.txt">Rows n = 0..30, flattened</a>

%e The first rows are:

%e     1

%e     1, 1

%e     1, 2, 1

%e     1, 3, 3, 1

%e     1, 4, 6, 4, 1

%e     1, 5, 1, 0, 1, 0, 5, 1

%e     1, 6, 6, 1, 1, 1, 5, 6, 1

%e     1, 7, 1, 2, 7, 2, 2, 6, 1, 1, 7, 1

%e     1, 8, 8, 3, 9, 9, 4, 8, 7, 2, 8, 8, 1

%e     1, 9, 1, 6, 1, 1, 1, 2, 1, 8, 1, 3, 1, 2, 1, 5, 9, 1, 0, 1, 6, 9, 1

%o (PARI) { r = [1]; for (n=0, 9, apply (v -> print1 (v ", "), r); d = concat(apply(v -> if (v, digits(v), [0]), r)); r = concat(apply(v -> if (v, di

%o gits(v), [0]), vector(#d+1, k, if (k==1, d[k], k==#d+1, d[#d], d[k-1]+d[k]))))) }

%Y See A339359 for a similar sequence.

%Y Cf. A007318, A093086.

%K nonn,base,tabf,easy

%O 0,5

%A _Rémy Sigrist_, Dec 02 2020