A137171 Interleaved reading of A000749 and its first to third differences.

0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 2, 1, 1, 3, 3, 1, 4, 6, 4, 2, 10, 10, 6, 6, 20, 16, 12, 16, 36, 28, 28, 36, 64, 56, 64, 72, 120, 120, 136, 136, 240, 256, 272, 256, 496, 528, 528, 496, 1024, 1056, 1024, 992, 2080, 2080, 2016, 2016, 4160, 4096, 4032, 4096, 8256, 8128, 8128

Offset: 0

Author

Paul Curtz, May 11 2008

Keywords

• nonn
• tabf

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).

Crossrefs

Cf. A137172, A137173.

Programs

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 *)

Extensions

Edited by R. J. Mathar, Jun 28 2008