|
|
A109436
|
|
Triangle of numbers: row n gives the elements along the subdiagonal of A109435 that connects 2^n with (n+2)*2^(n-1).
|
|
2
|
|
|
0, 0, 1, 1, 2, 3, 4, 7, 8, 8, 15, 19, 20, 16, 31, 43, 47, 48, 32, 63, 94, 107, 111, 112, 64, 127, 201, 238, 251, 255, 256, 128, 255, 423, 520, 558, 571, 575, 576, 256, 511, 880, 1121, 1224, 1262, 1275, 1279, 1280, 512, 1023, 1815, 2391, 2656, 2760, 2798, 2811
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,5
|
|
COMMENTS
|
In the limit of row number n->infinity, the differences of the n-th row of the table, read from right to left, are 1, 4, 13, 38, 104,... = A084851.
|
|
LINKS
|
|
|
EXAMPLE
|
1;
2, 1;
4, 3, 1;
8, 7, 3, 1;
16, 15, 8, 3, 1;
32, 31, 19, 8, 3, 1;
64, 63, 43, 20, 8, 3, 1;
128, 127, 94, 47, 20, 8, 3, 1;
If we read this triangle starting at 2^n in its first column along its n-th subdiagonal up to the first occurrence of (n+2)*2^(n-1), we get row n of the current triangle, which begins:
0, 0;
1, 1;
2, 3;
4, 7, 8;
8, 15, 19, 20;
16, 31, 43, 47, 48;
32, 63, 94, 107, 111, 112;
|
|
MATHEMATICA
|
T[n_, m_] := Length[ Select[ StringPosition[ #, StringDrop[ ToString[10^m], 1]] & /@ Table[ ToString[ FromDigits[ IntegerDigits[i, 2]]], {i, 2^n, 2^(n + 1) - 1}], # != {} &]]; Flatten[ Table[ T[n + i, i], {n, 0, 9}, {i, 0, n}]]
|
|
CROSSREFS
|
|
|
KEYWORD
|
base,nonn,tabf
|
|
AUTHOR
|
_Robert G. Wilson v_, Jun 28 2005
|
|
EXTENSIONS
|
Edited by _R. J. Mathar_, Nov 17 2009
|
|
STATUS
|
approved
|
|
|
|