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Search: id:A137171
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| A137171 |
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Interleaved reading of A000749 and its first to third differences. |
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+0
2
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| 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; listen)
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OFFSET
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0,11
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COMMENT
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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 1st 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.
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CROSSREFS
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Cf. A137172, A137173.
Adjacent sequences: A137168 A137169 A137170 this_sequence A137172 A137173 A137174
Sequence in context: A124054 A082870 A026009 this_sequence A010356 A100640 A144401
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KEYWORD
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nonn,tabf
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AUTHOR
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Paul Curtz (bpcrtz(AT)free.fr), May 11 2008
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EXTENSIONS
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Edited by R. J. Mathar, Jun 28 2008
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