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A003988
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Triangle with subscripts (1,1),(2,1),(1,2),(3,1),(2,2),(1,3), etc. in which entry (i,j) is [ i/j ].
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4
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1, 2, 0, 3, 1, 0, 4, 1, 0, 0, 5, 2, 1, 0, 0, 6, 2, 1, 0, 0, 0, 7, 3, 1, 1, 0, 0, 0, 8, 3, 2, 1, 0, 0, 0, 0, 9, 4, 2, 1, 1, 0, 0, 0, 0, 10, 4, 2, 1, 1, 0, 0, 0, 0, 0, 11, 5, 3, 2, 1, 1, 0, 0, 0, 0, 0, 12, 5, 3, 2, 1, 1, 0, 0, 0, 0, 0, 0, 13, 6, 3, 2, 1, 1, 1, 0, 0, 0, 0, 0, 0, 14, 6, 4, 2, 2, 1, 1, 0, 0, 0, 0
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,2
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COMMENTS
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Another version of A010766.
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LINKS
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Reinhard Zumkeller, Table of n, a(n) for n = 1..5050
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FORMULA
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T(n,k) = sum_{i=1}^k A077049(n,i). G.f. sum_{k>0} x^k y^k/(1-x^k) / (1-x) = sum_{k>0} x^k y / (1 - x^k y) / (1-x) = sum_{k>0} x^k sum_{d|k} y^d / (1-x) = A(x,y)/(1-x) where A(x,y) is the g.f. of A077049. - Franklin T. Adams-Watters, Jan 28 2006
T(n,k) = floor((n + 1 - k) / k). [Reinhard Zumkeller, Apr 13 2012]
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MATHEMATICA
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t[n_, k_] := Quotient[n, k]; Table[t[n-k+1, k], {n, 1, 14}, {k, 1, n}] // Flatten (* Jean-François Alcover, Nov 21 2013 *)
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PROG
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(Haskell)
a003988 n k = (n + 1 - k) `div` k
a003988_row n = zipWith div [n, n-1..1] [1..n]
a003988_tabl = map a003988_row [1..]
-- Reinhard Zumkeller, Apr 13 2012
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CROSSREFS
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Cf. A003056, A049581, A003991, A004247.
Row sums are in A006218. Antidiagonal sums are in A002541.
Sequence in context: A220645 A127374 A098862 * A185914 A144257 A257232
Adjacent sequences: A003985 A003986 A003987 * A003989 A003990 A003991
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KEYWORD
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tabl,nonn,easy,nice
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AUTHOR
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Marc LeBrun
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EXTENSIONS
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More terms from James A. Sellers
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STATUS
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approved
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