A098564 Numbers that appear as binomial coefficients exactly 4 times.

10, 15, 21, 28, 35, 36, 45, 55, 56, 66, 78, 84, 91, 105, 126, 136, 153, 165, 171, 190, 220, 231, 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, 820

Offset: 1

Author

Paul D. Hanna, Oct 27 2004

Keywords

• nonn

Comments

Let f(k) be the sequence of numbers that appear as binomial coefficients exactly k times:

f(1) = {2}.

f(2) = A137905.

f(3) appears to be A000984 \ {1, 2}: central binomial coefficients greater than 2.

f(4) = this sequence.

f(5) appears to be empty.

f(6) = A098565.

f(7) appears to be empty.

f(8) begins with 3003.

Links

• T. D. Noe, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000984, A098565, A137905.

Programs

Mathematica

binmax = 10^5; dm = 100; Clear[f]; f[m_] := f[m] = (Join[Table[Binomial[n, k], {n, 1, m}, {k, 1, n-1}], Table[Table[{Binomial[n, 1], Binomial[n, 2]}, {2}], {n, m+1, binmax}]] // Flatten // Tally // Select[#, #[[1]] <= binmax && #[[2]] == 4&]&)[[All, 1]] // Sort; f[dm]; f[m = 2*dm]; While[f[m] != f[m-dm], Print[m]; m = m+dm]; f[m] (* Jean-François Alcover, Mar 10 2014 *)