A182237 Numbers occurring exactly in 2 rows of Pascal's triangle.

6, 10, 15, 20, 21, 28, 35, 36, 45, 55, 56, 66, 70, 78, 84, 91, 105, 126, 136, 153, 165, 171, 190, 220, 231, 252, 253, 276, 286, 300, 325, 330, 351, 364, 378, 406, 435, 455, 462, 465, 495, 496, 528, 560, 561, 595, 630, 666, 680, 703, 715, 741, 780, 792, 816

Offset: 1

Author

Reinhard Zumkeller, Dec 24 2012

Keywords

• nonn

Comments

A059233(a(n)) = 2.

Links

• Reinhard Zumkeller and T. D. Noe, Table of n, a(n) for n = 1..1000 (first 100 terms from Reinhard Zumkeller)
• Wikipedia, Singmaster's conjecture
• Index entries for triangles and arrays related to Pascal's triangle

Crossrefs

Cf. A098565.

Programs

Haskell

import Data.List (elemIndices)
a182237 n = a182237_list !! (n-1)
a182237_list = map (+ 2 ) $ elemIndices 2 a059233_list

Mathematica

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 *)