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A002501 a(n) = 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 théorème s'applique notamment au dénombrement des relations binaires externes qui possèdent la propriété de connexité; cela revient à calculer le nombre a(m,n) de manières de remplir un tableau de m lignes et n colonnes avec des 0 et des 1, en respectant les deux conditions suivantes: (1): aucune rangée (ligne ni colonne) ne doit être tout entière remplie de zéros; (2): deux cases quelconques marquées 1 peuvent être jointes par une chaîne de cases marquées 1 telle que deux cases consécutives de la chaîne appartiennent à une même rangée."

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 dénombrement 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

a(n) = 14*a(n-1)-61*a(n-2)+84*a(n-3). - Wesley Ivan Hurt, Apr 11 2022

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 October 2 17:44 EDT 2022. Contains 357228 sequences. (Running on oeis4.)