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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 Central binomial coefficients c = A000984(n) > 1 appear once in the middle column C(2n, n), and thereafter in one or more later rows to the left as C(r,k) and to the right as C(r, r-k), k < r/2; the last time in row r = c = C(c,1) = C(c,c-1). For these, a(n) = (A003016(n)+1)/2. For all other numbers n > 1, a(n) = A003016(n)/2. - M. F. Hasler, Mar 01 2023 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 FORMULA 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 a(n) = ceiling(A003016(n)/2). - M. F. Hasler, Mar 01 2023 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-François 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 (PARI) A059233(n)=A003016(n)\/2 \\ M. F. Hasler, Mar 01 2023 CROSSREFS Cf. A003016, A003015. Sequence in context: A256554 A321649 A003650 * A357327 A327924 A354057 Adjacent sequences: A059230 A059231 A059232 * A059234 A059235 A059236 KEYWORD easy,nice,nonn AUTHOR Fabian Rothelius, Jan 20 2001 STATUS approved

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