OFFSET
0,11
COMMENTS
A000749 is identical to its fourth differences, which implies that the 2nd differences equal the 5th, the 3rd differences the 6th and so on and implies that each of the sequences of these differences obeys the recurrence a(n)=4a(n-1)-6a(n-2)+4a(n-3), n > 3.
The table containing A000749 and its first differences (essentially A038505), 2nd differences (A038504) and 3rd differences (A038503) as the 4 rows is
O, 0, 0, 1, 4, 10, 20, 36, 64, ...
0, 0, 1, 3, 6, 10, 16, 28, 56, ...
0, 1, 2, 3, 4, 6, 12, 28, 64, ...
1, 1, 1, 1, 2, 6, 16, 36, 72, ...
Columns sums are 1, 2, 4, 8, 16, 32 ... = 2^n =A000079. The sequence reads this table column by column.
LINKS
Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 4, 0, 0, 0, -6, 0, 0, 0, 4).
MATHEMATICA
Join[{0, 0, 0, 1}, LinearRecurrence[{0, 0, 0, 4, 0, 0, 0, -6, 0, 0, 0, 4}, {0, 0, 1, 1, 0, 1, 2, 1, 1, 3, 3, 1}, 59]] (* Ray Chandler, Sep 23 2015 *)
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Paul Curtz, May 11 2008
EXTENSIONS
Edited by R. J. Mathar, Jun 28 2008
STATUS
approved