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A059233 Number of rows in which n appears in Pascal's triangle (A007318). 9
1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,5

COMMENTS

a(A180058(n)) = n and a(m) < n for m < A180058(n); a(A182237(n)) = 2; a(A098565(n)) = 3. - Reinhard Zumkeller, Dec 24 2012

REFERENCES

L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 93, #47.

C. S. Ogilvy, Tomorrow's Math. 2nd ed., Oxford Univ. Press, 1972, p. 96.

LINKS

T. D. Noe, Table of n, a(n) for n=2..10000

D. Singmaster, How often does an integer occur as a binomial coefficient?, Amer. Math. Monthly, 78 (1971), 385-386.

Eric Weisstein's World of Mathematics, Pascal's Triangle

Wikipedia, Singmaster's conjecture

Index entries for triangles and arrays related to Pascal's triangle

EXAMPLE

6 appears in both row 4 and row 6 in Pascal's triangle, therefore a(6)=2.

MATHEMATICA

nmax = 101; A007318 = Table[Binomial[n, k], {n, 0, nmax}, {k, 0, n}]; a[n_] := Position[A007318, n][[All, 1]] // Union // Length; Table[a[n], {n, 2, nmax}] (* Jean-Fran├žois Alcover, Sep 09 2013 *)

PROG

(Haskell)

a059233 n = length $ filter (n `elem`) $

                            take (fromInteger n) $ tail a007318_tabl

a059233_list = map a059233 [2..]

-- Reinhard Zumkeller, Dec 24 2012

CROSSREFS

Cf. A003016, A003015.

Sequence in context: A256067 A256554 A003650 * A143898 A238747 A101873

Adjacent sequences:  A059230 A059231 A059232 * A059234 A059235 A059236

KEYWORD

easy,nice,nonn

AUTHOR

Fabian Rothelius, Jan 20 2001

STATUS

approved

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Last modified November 13 13:15 EST 2018. Contains 317149 sequences. (Running on oeis4.)