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A130168 (b(n)+b(n+1))/3, where b(n) = A000366(n). +0
3
1, 3, 15, 111, 1131, 15123, 256335, 5364471, 135751731, 4084163643, 144039790455, 5884504366431, 275643776229531, 14673941326078563, 880908054392169375, 59226468571935857991, 4432461082611507366531, 367227420727722013775883, 33514867695588319595233095 (list; graph; listen)
OFFSET

2,2

COMMENT

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'\'elimination, m\'ethode de parall\'elogramme, Annales de la Facult\'e des Sciences de Marseille, XI (1901), 141-164.

CROSSREFS

Cf. A000366, A130169.

Adjacent sequences: A130165 A130166 A130167 this_sequence A130169 A130170 A130171

Sequence in context: A109498 A112936 A001063 this_sequence A089945 A135083 A058104

KEYWORD

nonn

AUTHOR

D. E. Knuth, Aug 02 2007

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Last modified October 6 12:54 EDT 2008. Contains 144667 sequences.


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