login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A130168 a(n) = (b(n) + b(n+1))/3, where b(n) = A000366(n). 3
1, 3, 15, 111, 1131, 15123, 256335, 5364471, 135751731, 4084163643, 144039790455, 5884504366431, 275643776229531, 14673941326078563, 880908054392169375, 59226468571935857991, 4432461082611507366531, 367227420727722013775883, 33514867695588319595233095 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,2

COMMENTS

As remarked by Gessel, A000366 has a combinatorial interpretation via a certain 2n X n array; this sequence is for a similar array of size (2n-1) X (n-1).

In effect, Dellac gives a combinatorial reason why the elements of A000366 are alternately -1 and +1 modulo 3. Dellac also shows that all the terms of this sequence are odd.

LINKS

Table of n, a(n) for n=2..20.

Hippolyte Dellac, Note sur l'élimination, méthode de parallélogramme, Annales de la Faculté des Sciences de Marseille, XI (1901), 141-164. [Warning 76 Mb; go to p. 81 in the pdf file]

FORMULA

G.f.: 2*(1+x)/(3*x^3)*Q(0) - 2/(3*x) - 1/x^2 - 2/(3*x^3), where Q(k) = 1 - x*(k+1)^2/( x*(k+1)^2 - 2/(1 - x*(k+1)^2/( x*(k+1)^2 - 2/Q(k+1) ))); (continued fraction). - Sergei N. Gladkovskii, Oct 22 2013

MATHEMATICA

b[n_] := (-2^(-1))^(n-2)*Sum[Binomial[n, k]*(1-2^(n+k+1))* BernoulliB[n+k+1], {k, 0, n}];

a[n_] := (b[n] + b[n+1])/3;

a /@ Range[2, 20] (* Jean-François Alcover, Apr 08 2021 *)

CROSSREFS

Cf. A000366, A130169.

Sequence in context: A254789 A112936 A001063 * A267083 A089945 A135083

Adjacent sequences:  A130165 A130166 A130167 * A130169 A130170 A130171

KEYWORD

nonn

AUTHOR

Don Knuth, Aug 02 2007

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 July 26 22:49 EDT 2021. Contains 346300 sequences. (Running on oeis4.)