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Search: id:A159927
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| A159927 |
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Triangle read by rows: a(1,1) = 1. a(m,m) = sum of all terms in rows 1 through m-1. a(m,n) = a(m-1,n) + (sum of all terms in rows 1 through m-1), for n < m. |
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+0
3
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| 1, 2, 1, 6, 5, 4, 25, 24, 23, 19, 135, 134, 133, 129, 110, 886, 885, 884, 880, 861, 751, 6784, 6783, 6782, 6778, 6759, 6649, 5898, 59115, 59114, 59113, 59109, 59090, 58980, 58229, 52331, 576527, 576526, 576525, 576521, 576502, 576392, 575641, 569743
(list; table; graph; listen)
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OFFSET
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1,2
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COMMENT
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A159928(m) = -A075374(m+4)+A075374(m+3), for m >= 1. -A075374(m+4) = the sum of all terms of triangle A159927 in rows 1 through m. A159928 contains the row-sums of triangle A159927.
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EXAMPLE
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The triangle starts like this:
1,
2,1,
6,5,4,
25,24,23,19
The sum of all of these terms is 110. Adding 110 to each term of the 4th row, we get: 25+110=135, 24+110=134, 23+110=133, 19+110=129, 0+110=110. So row 5 is 135,134,133,129,110.
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MAPLE
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A159927 := proc(n, m) option remember; local rs; if n = 1 then 1; else rs := add(add( procname(i, j), j=1..i), i=1..n-1) ; if n = m then rs; else procname(n-1, m)+rs; fi; fi; end: for n from 1 to 10 do for m from 1 to n do printf("%d, ", A159927(n, m)) ; od: od: [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 28 2009]
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CROSSREFS
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Cf. A159924, A159928, A075374
Sequence in context: A118980 A090665 A021826 this_sequence A105225 A011018 A156993
Adjacent sequences: A159924 A159925 A159926 this_sequence A159928 A159929 A159930
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KEYWORD
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nonn,tabl
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AUTHOR
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Leroy Quet (q1qq2qqq3qqqq(AT)yahoo.com), Apr 26 2009
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EXTENSIONS
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More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 28 2009
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