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 A137171 Interleaved reading of A000749 and its first to third differences. 2
 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 (list; graph; refs; listen; history; text; internal format)
 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 Cf. A137172, A137173. Sequence in context: A334187 A082870 A026009 * A010356 A100640 A242779 Adjacent sequences:  A137168 A137169 A137170 * A137172 A137173 A137174 KEYWORD nonn,tabf AUTHOR Paul Curtz, May 11 2008 EXTENSIONS Edited by R. J. Mathar, Jun 28 2008 STATUS approved

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Last modified May 21 18:55 EDT 2022. Contains 353926 sequences. (Running on oeis4.)