|
|
A339359
|
|
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 [d_0, d_0+d_1, d_1+d_2, ..., d_{k-1}+d_k, d_k].
|
|
1
|
|
|
1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 4, 6, 4, 1, 1, 5, 10, 10, 5, 1, 1, 6, 6, 1, 1, 1, 5, 6, 1, 1, 7, 12, 7, 2, 2, 6, 11, 7, 1, 1, 8, 8, 3, 9, 9, 4, 8, 7, 2, 8, 8, 1, 1, 9, 16, 11, 12, 18, 13, 12, 15, 9, 10, 16, 9, 1, 1, 10, 10, 7, 7, 2, 2, 3, 3, 9, 9, 4, 4, 3, 3, 6, 14, 10, 1, 1, 7, 15, 10, 1
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,5
|
|
COMMENTS
|
This sequence combines features of Pascal's triangle (A007318) and of A214365.
Rows 0 to 5 match that of Pascal's triangle, thereafter the values differ.
Every column is eventually periodic.
|
|
LINKS
|
|
|
EXAMPLE
|
The first rows are:
1
1, 1
1, 2, 1
1, 3, 3, 1
1, 4, 6, 4, 1
1, 5, 10, 10, 5, 1
1, 6, 6, 1, 1, 1, 5, 6, 1
1, 7, 12, 7, 2, 2, 6, 11, 7, 1
1, 8, 8, 3, 9, 9, 4, 8, 7, 2, 8, 8, 1
1, 9, 16, 11, 12, 18, 13, 12, 15, 9, 10, 16, 9, 1
|
|
PROG
|
(PARI) { r=[1]; for (n=0, 10, apply (v -> print1(v", "), r); d=concat(apply(digits, r)); r=vector(#d+1, k, if (k==1, d[1], k==#d+1, d[#d], d[k-1]+d[k]))) }
|
|
CROSSREFS
|
See A339379 for a similar sequence.
|
|
KEYWORD
|
nonn,base,tabf,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|