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A003988 Triangle with subscripts (1,1),(2,1),(1,2),(3,1),(2,2),(1,3), etc. in which entry (i,j) is [ i/j ]. 5
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)
OFFSET
1,2
COMMENTS
Another version of A010766.
LINKS
FORMULA
From Franklin T. Adams-Watters, Jan 28 2006: (Start)
T(n,k) = Sum_{i=1..k} A077049(n,i).
G.f.: (1/(1-x))*Sum_{k>0} x^k*y^k/(1-x^k) = (1/(1-x))*Sum_{k>0} x^k * y / (1 - x^k y) = (1/(1-x)) * Sum_{k>0} x^k * Sum_{d|k} y^d = A(x,y)/(1-x) where A(x,y) is the g.f. of A077049. (End)
T(n,k) = floor((n + 1 - k) / k). - Reinhard Zumkeller, Apr 13 2012
MATHEMATICA
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 *)
PROG
(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
CROSSREFS
Row sums are in A006218. Antidiagonal sums are in A002541.
Sequence in context: A220645 A127374 A098862 * A185914 A144257 A257232
KEYWORD
tabl,nonn,easy,nice
AUTHOR
EXTENSIONS
More terms from James A. Sellers
STATUS
approved

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Last modified March 19 01:34 EDT 2024. Contains 370952 sequences. (Running on oeis4.)