The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A115246 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A115246

Number of different ways to select n elements from three sets of n elements such that there is at least one element from each set.
(history; published version)

#16 by Charles R Greathouse IV at Thu Sep 08 08:45:23 EDT 2022

PROG

(MAGMAMagma) [Binomial(3*n, n)-3*Binomial(2*n, n)+3: n in [1..40]]; // Vincenzo Librandi, Feb 09 2016

Discussion

Thu Sep 08

08:45

OEIS Server: https://oeis.org/edit/global/2944

#15 by N. J. A. Sloane at Sat Feb 13 23:20:24 EST 2016

STATUS

proposed

approved

#14 by Michel Marcus at Fri Feb 12 07:29:33 EST 2016

STATUS

editing

proposed

#13 by Michel Marcus at Fri Feb 12 07:29:27 EST 2016

FORMULA

a(n) = binomial(3n, n) - 3*binomial(2n, n) + 3.

G.f.: (1/((x-1)sqrt(a*b)))*[3*sqrt(a)*(1-x) - 3*sqrt(a*b) - 2*(1-x)*sqrt(b)*cos(c/3)], where a = 4-27*x, b = 1-4*x, c = arcsin{(3*sqrt(3*x)/2). (End)

STATUS

proposed

editing

#12 by Vincenzo Librandi at Tue Feb 09 02:54:14 EST 2016

STATUS

editing

proposed

Discussion

Tue Feb 09

06:18

Joerg Arndt: Curly brace at arcsin is unmatched.

#11 by Vincenzo Librandi at Tue Feb 09 02:54:01 EST 2016

DATA

0, 0, 27, 288, 2250, 15795, 105987, 696864, 4540968, 29490750, 191420427, 1243565235, 8091223647, 52739879283, 344402073027, 2253045672480, 14764068268068, 96899123172708, 636877933530303, 4191430966219038, 27617820628739718, 182176855684869243

PROG

(MAGMA) [Binomial(3*n, n)-3*Binomial(2*n, n)+3: n in [1..40]]; // Vincenzo Librandi, Feb 09 2016

STATUS

proposed

editing

#10 by Michel Marcus at Tue Feb 09 00:29:42 EST 2016

STATUS

editing

proposed

#9 by Michel Marcus at Tue Feb 09 00:29:36 EST 2016

FORMULA

From G. C. Greubel, Feb 08, 2016: (Start)

STATUS

proposed

editing

#8 by G. C. Greubel at Mon Feb 08 19:29:35 EST 2016

STATUS

editing

proposed

#7 by G. C. Greubel at Mon Feb 08 19:29:17 EST 2016

LINKS

G. C. Greubel, <a href="/A115246/b115246.txt">Table of n, a(n) for n = 1..1000</a>

FORMULA

From G. C. Greubel, Feb 08, 2016: (Start)

E.g.f.: 3*exp(x) - 3*exp(2*x)*BesselI_{0}(2*x) + Hypergeometric2F2[1/3,2/3; 1/2,1; 27*x/4].

G.f.: (1/((x-1)sqrt(a*b)))*[3*sqrt(a)*(1-x) - 3*sqrt(a*b) - 2*(1-x)*sqrt(b)*cos(c/3)], where a = 4-27*x, b = 1-4*x, c = arcsin{3*sqrt(3*x)/2). (End)

MATHEMATICA

Table[Binomial[3 n, n] - 3*Binomial[2 n, n] + 3, {n, 1, 100}] (* G. C. Greubel, Feb 08 2016 *)

KEYWORD

nonn,changed

STATUS

approved

editing