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

0,11

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

Table of n, a(n) for n=0..62.

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

Cf. A137172, A137173.

Sequence in context: A334187 A082870 A026009 * A010356 A100640 A242779

Adjacent sequences: A137168 A137169 A137170 * A137172 A137173 A137174

Keyword

nonn,tabf,changed

Author

Paul Curtz, May 11 2008

Extensions

Edited by R. J. Mathar, Jun 28 2008

Status

approved