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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 ]. 4
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

Reinhard Zumkeller, Table of n, a(n) for n = 1..5050

FORMULA

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]

MATHEMATICA

t[n_, k_] := Quotient[n, k]; Table[t[n-k+1, k], {n, 1, 14}, {k, 1, n}] // Flatten (* Jean-Fran├žois 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

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

KEYWORD

tabl,nonn,easy,nice

AUTHOR

Marc LeBrun

EXTENSIONS

More terms from James A. Sellers

STATUS

approved

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Last modified October 24 01:20 EDT 2018. Contains 316541 sequences. (Running on oeis4.)