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A002501 7^n - 3*4^n + 2*3^n.
(Formerly M5078 N2197)
17
1, 19, 205, 1795, 14221, 106819, 778765, 5581315, 39606541, 279447619, 1965098125, 13792018435, 96690872461, 677427332419, 4744368982285, 33220131761155, 232579232659981, 1628208214321219, 11398072876175245, 79788974736297475, 558532690864457101 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Counts connected relations. On page 578 Kreweras (1969) says: "Le theoreme s'applique notamment au denombrement des relations binaires externes qui possedent la propriete de connexite; cela revient a calculer le nombre a(m,n) de manieres de remplier un tableau de m lignes et n colonnes avec des 0 et des 1, en respectant les deux conditions suivantes: 1: aucune rangee (ligne ni colonne) ne doit etre tout entiere remplie de zeros; (2): deux cases quelconques marquees 1 peuvent etre jointes par une chaine de cases marquees 1 telle que deux cases consecutives de la chaine appartiennent a une meme rangee."

REFERENCES

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

T. D. Noe, Table of n, a(n) for n = 1..200

G. Kreweras, Inversion des polynomes de Bell bidimensionnels et application au denombrement des relations binaires connexes. C. R. Acad. Sci. Paris Ser. A-B 268 1969 A577-A579.

Index entries for linear recurrences with constant coefficients, signature (14,-61,84)

FORMULA

G.f. -x*(1+5*x) / ( (3*x-1)*(7*x-1)*(4*x-1) ). - R. J. Mathar, Jun 09 2013

MATHEMATICA

Table[7^n - 3*4^n + 2*3^n, {n, 20}] (* T. D. Noe, May 29 2012 *)

PROG

(PARI) a(n)=7^n-3*4^n+2*3^n \\ Charles R Greathouse IV, Sep 24 2015

CROSSREFS

Cf. A005333, A001047, A002502, A093732, A093733.

A diagonal of A262307.

Sequence in context: A113596 A155670 A085770 * A180364 A125407 A289423

Adjacent sequences:  A002498 A002499 A002500 * A002502 A002503 A002504

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane.

EXTENSIONS

Better definition and more terms from Goran Kilibarda, Vladeta Jovovic, Apr 14 2004

STATUS

approved

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Last modified January 18 18:48 EST 2018. Contains 297864 sequences.