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A098564 Numbers that appear as binomial coefficients exactly 4 times. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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) = A000984 (central binomial coefficients) except for first 2 terms: {1,2}.

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

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-Fran├žois Alcover, Mar 10 2014 *)

CROSSREFS

Cf. A000984, A098565, A137905.

Sequence in context: A108614 A115708 A068992 * A168103 A322045 A062691

Adjacent sequences:  A098561 A098562 A098563 * A098565 A098566 A098567

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Oct 27 2004

STATUS

approved

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Last modified July 19 09:33 EDT 2019. Contains 325155 sequences. (Running on oeis4.)