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A130168 a(n) = (b(n) + b(n+1))/3, where b(n) = A000366(n). 2
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.

REFERENCES

Hippolyte Dellac, Note sur l'élimination, méthode de parallélogramme, Annales de la Faculté des Sciences de Marseille, XI (1901), 141-164.

LINKS

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

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

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

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Last modified August 12 17:17 EDT 2020. Contains 336439 sequences. (Running on oeis4.)