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Search: id:A064865
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| A064865 |
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Fill a triangular array by rows by writing numbers 1, then 1 up to 2^2, then 1 up to 3^2, then 1 up to 4^2 and so on. The final elements of the rows form the sequence. |
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17
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| 1, 2, 1, 5, 1, 7, 14, 6, 15, 25, 11, 23, 36, 14, 29, 45, 13, 31, 50, 6, 27, 49, 72, 15, 40, 66, 93, 21, 50, 80, 111, 22, 55, 89, 124, 16, 53, 91, 130, 1, 42, 84, 127, 171, 20, 66, 113, 161, 210, 35, 86, 138, 191, 245, 44, 100, 157, 215, 274, 45, 106, 168, 231, 295, 36
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Does every number appear at least once? Do some numbers like 1 appear infinitely often? - Robert G. Wilson v (rgwv(AT)rgwv.com), Oct 10 2001
Difference between n-th triangular number and largest square pyramidal number (A000330) less than it. - Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Sep 11 2006
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FORMULA
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a(n) = n(n+1)/2 - max_{p(m) < n(n+1)/2} p(m), where p(m) = m(m+1)(2m+1)/6. - Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Sep 11 2006
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EXAMPLE
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The triangle begins:
....1
...1.2
..3.4.1
.2.3.4.5
6.7.8.9.1
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MATHEMATICA
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a = {}; Do[a = Append[a, Table[i, {i, 1, n^2} ]], {n, 1, 100} ]; a = Flatten[a]; Do[Print[a[[n(n + 1)/2]]], {n, 1, 100} ]
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CROSSREFS
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Table: A064866.
Cf. A000217, A000330.
Sequence in context: A014648 A036073 A124227 this_sequence A093127 A115123 A132081
Adjacent sequences: A064862 A064863 A064864 this_sequence A064866 A064867 A064868
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KEYWORD
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easy,nonn
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AUTHOR
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Floor van Lamoen (fvlamoen(AT)hotmail.com), Oct 08 2001
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EXTENSIONS
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More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Oct 10 2001
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