login
This site is supported by donations to The OEIS Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A279054 Largest integer m for which binomial(m,n-1) > binomial(m-1,n). 1
1, 4, 7, 9, 12, 14, 17, 20, 22, 25, 28, 30, 33, 35, 38, 41, 43, 46, 49, 51, 54, 56, 59, 62, 64, 67, 69, 72, 75, 77, 80, 83, 85, 88, 90, 93, 96, 98, 101, 103, 106, 109, 111, 114, 117, 119, 122, 124, 127, 130, 132, 135, 138, 140, 143, 145, 148, 151, 153, 156, 158, 161, 164, 166, 169, 172, 174, 177, 179 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Equivalently, a(n) is also the largest integer m for which C(m-1,n-2) + C(m-1,n-1) > C(m-1,n) in the (m-1)st row of Pascal's triangle.

Equivalently, a(n) is the largest integer m for which m*n > (m-n)*(m-n+1). - Robert Israel, Dec 05 2016

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = (3n-1+sqrt(5n^2-2n+1))/2 - 1 if 5n^2-2n+1 is a perfect square, else a(n) = floor((3n-1+sqrt(5n^2-2n+1))/2).

a(n) = ceiling((3*n - 3 + sqrt(5*n^2-2*n+1))/2). - Robert Israel, Dec 05 2016

(3/2+sqrt(5)/2)*n - 2 < f(n) < (3/2+sqrt(5)/2)*t. - Robert Israel, Dec 22 2016

EXAMPLE

a(1) = 1, since C(m,0) = 1 > m-1 = C(m-1,1) when m = 1 and C(m,0) <= C(m-1,1) when m >= 2.

a(2) = 4, since C(m,1) = m > (m-1)(m-2)/2 = C(m-1,2) when 1 <= m <= 4 and C(m,1) < C(m-1,2) when m >= 5.

a(3) = 7, since C(m,2) = m(m-1)/2 >= (m-1)(m-2)(m-3)/6 = C(m-1,3) when 1 <= m <= 7 and C(m,2) < C(m-1,3) when m >= 8.

MAPLE

seq(ceil((3*n - 3 + sqrt(5*n^2-2*n+1))/2), n=1..100); # Robert Israel, Dec 05 2016

MATHEMATICA

Table[Ceiling[(3 n - 3 + Sqrt[5 n^2 - 2 n + 1]) / 2], {n, 60}] (* Vincenzo Librandi, Dec 05 2016 *)

PROG

(MAGMA) [Ceiling((3*n-3+Sqrt(5*n^2-2*n+1))/2): n in [1..70]]; // Vincenzo Librandi, Dec 05 2016

CROSSREFS

Sequence in context: A186323 A007064 A007073 * A086824 A266936 A080574

Adjacent sequences:  A279051 A279052 A279053 * A279055 A279056 A279057

KEYWORD

nonn

AUTHOR

Timothy L. Tiffin, Dec 04 2016

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 14 05:36 EST 2019. Contains 329978 sequences. (Running on oeis4.)