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A052934 Expansion of (1-x)/(1-6*x). 13
1, 5, 30, 180, 1080, 6480, 38880, 233280, 1399680, 8398080, 50388480, 302330880, 1813985280, 10883911680, 65303470080, 391820820480, 2350924922880, 14105549537280, 84633297223680, 507799783342080 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

With formula a(n) = (5*6^n + 0^n)/6, this is the binomial transform of A083425. - Paul Barry, Apr 30 2003

For n>=1, a(n) is equal to the number of functions f:{1,2...,n}->{1,2,3,4,5,6} such that for a fixed x in {1,2,...,n} and a fixed y in {1,2,3,4,5,6} we have f(x) != y. - Aleksandar M. Janjic and Milan Janjic, Mar 27 2007

a(n) = (n+1) terms in the sequence (1, 4, 5, 5, 5, ...) dot (n+1) terms in the sequence (1, 1, 5, 30, 180, 1080, ...). Example: a(4) = (1, 4, 5, 5, 5) dot (1, 1, 5, 30, 180) = (1 + 4 + 25 + 150 + 900), where (1, 4, 25, 150,...) = first differences of current sequence. - Gary W. Adamson, Aug 03 2010

a(n) is the number of compositions of n when there are 5 types of each natural number. - Milan Janjic, Aug 13 2010

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 922

Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets

Index entries for linear recurrences with constant coefficients, signature (6).

FORMULA

a(n) = 6*a(n-1), n>=2.

a(n) = 5*6^(n-1), n>=1. - Vincenzo Librandi, Sep 15 2011

G.f.: (1-x)/(1-6*x).

G.f.: 1/(1 - 5*Sum_{k>=1} x^k).

E.g.f.: (1/6)*(1 + 5*exp(6*x)). - Stefano Spezia, Oct 18 2019

MAPLE

spec := [S, {S=Sequence(Prod(Sequence(Z), Union(Z, Z, Z, Z, Z)))}, unlabeled ]: seq(combstruct[count ](spec, size=n), n=0..20);

seq(`if`(n=0, 1, 5*6^(n-1)), n=0..30); # G. C. Greubel, Oct 18 2019

MATHEMATICA

Join[{1}, NestList[6#&, 5, 20]] (* Harvey P. Dale, Nov 30 2015 *)

PROG

(PARI) vector(31, n, if(n==1, 1, 5*6^(n-2))) \\ G. C. Greubel, Oct 18 2019

(MAGMA) [1] cat [5*6^(n-1): n in [1..30]]; // G. C. Greubel, Oct 18 2019

(MAGMA) R<x>:=PowerSeriesRing(Integers(), 22); Coefficients(R!( (1-x)/(1-6*x))); // Marius A. Burtea, Oct 18 2019

(Sage) [1]+[5*6^(n-1) for n in (1..30)] # G. C. Greubel, Oct 18 2019

(GAP) Concatenation([1], List([1..30], n-> 5*6^(n-1) )); # G. C. Greubel, Oct 18 2019

CROSSREFS

Cf. A083425.

Sequence in context: A242157 A094167 A051738 * A136785 A227383 A155195

Adjacent sequences:  A052931 A052932 A052933 * A052935 A052936 A052937

KEYWORD

easy,nonn

AUTHOR

encyclopedia(AT)pommard.inria.fr, Jan 25 2000

STATUS

approved

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Last modified June 19 15:47 EDT 2021. Contains 345142 sequences. (Running on oeis4.)