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A339379 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].

%I A339379 #16 Aug 19 2025 08:47:13
%S A339379 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 A339379 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 A339379 3,1,2,1,5,9,1,0,1,6,9,1
%N A339379 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 A339379 This sequence combines features of Pascal's triangle (A007318) and of A093086.
%C A339379 Rows 0 to 4 match that of Pascal's triangle, thereafter the values differ.
%C A339379 Every column is eventually periodic.
%H A339379 Alois P. Heinz, <a href="/A339379/b339379.txt">Rows n = 0..30, flattened</a>
%e A339379 The first rows are:
%e A339379     1
%e A339379     1, 1
%e A339379     1, 2, 1
%e A339379     1, 3, 3, 1
%e A339379     1, 4, 6, 4, 1
%e A339379     1, 5, 1, 0, 1, 0, 5, 1
%e A339379     1, 6, 6, 1, 1, 1, 5, 6, 1
%e A339379     1, 7, 1, 2, 7, 2, 2, 6, 1, 1, 7, 1
%e A339379     1, 8, 8, 3, 9, 9, 4, 8, 7, 2, 8, 8, 1
%e A339379     1, 9, 1, 6, 1, 1, 1, 2, 1, 8, 1, 3, 1, 2, 1, 5, 9, 1, 0, 1, 6, 9, 1
%t A339379 NestList[Flatten[IntegerDigits[Map[Total, Partition[#, 2, 1, {-1, 1}, 0]]]] &, {1}, 10] (* _Paolo Xausa_, Aug 19 2025 *)
%o A339379 (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 A339379 gits(v), [0]), vector(#d+1, k, if (k==1, d[k], k==#d+1, d[#d], d[k-1]+d[k]))))) }
%Y A339379 See A339359 for a similar sequence.
%Y A339379 Cf. A007318, A093086.
%K A339379 nonn,base,tabf,easy
%O A339379 0,5
%A A339379 _Rémy Sigrist_, Dec 02 2020