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Numbers occurring exactly in 2 rows of Pascal's triangle.
6

%I #14 Mar 13 2013 18:53:04

%S 6,10,15,20,21,28,35,36,45,55,56,66,70,78,84,91,105,126,136,153,165,

%T 171,190,220,231,252,253,276,286,300,325,330,351,364,378,406,435,455,

%U 462,465,495,496,528,560,561,595,630,666,680,703,715,741,780,792,816

%N Numbers occurring exactly in 2 rows of Pascal's triangle.

%C A059233(a(n)) = 2.

%H Reinhard Zumkeller and T. D. Noe, <a href="/A182237/b182237.txt">Table of n, a(n) for n = 1..1000</a> (first 100 terms from Reinhard Zumkeller)

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Singmaster&#39;s_conjecture">Singmaster's conjecture</a>

%H <a href="/index/Pas#Pascal">Index entries for triangles and arrays related to Pascal's triangle</a>

%t nn = 1000; t = Table[s = {}; k = 1; While[k++; b = Binomial[n, k]; k <= n/2 && b <= nn, AppendTo[s, b]]; s, {n, nn}]; t2 = Select[t, Length[#] > 0 &]; Transpose[Select[Tally[Sort[Flatten[t2]]], #[[2]] == 1 &]][[1]] (* _T. D. Noe_, Mar 13 2013 *)

%o (Haskell)

%o import Data.List (elemIndices)

%o a182237 n = a182237_list !! (n-1)

%o a182237_list = map (+ 2 ) $ elemIndices 2 a059233_list

%Y Cf. A098565.

%K nonn

%O 1,1

%A _Reinhard Zumkeller_, Dec 24 2012