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A135518 Generalized repunits in base 15. 36
1, 16, 241, 3616, 54241, 813616, 12204241, 183063616, 2745954241, 41189313616, 617839704241, 9267595563616, 139013933454241, 2085209001813616, 31278135027204241, 469172025408063616, 7037580381120954241 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Primes in this sequence are given in A006033.

Let A be the Hessenberg matrix of order n, defined by: A[1,j]=1, A[i,i]:=15, (i>1), A[i,i-1]=-1, and A[i,j]=0 otherwise. Then, for n>=1, a(n)=det(A). - Milan Janjic, Feb 21 2010

Partial sums are in A014898. Also, the sequence is related to A014930 by A014930(n) = n*a(n) - Sum_{i=1..n-1}( a(i) ). - Bruno Berselli, Nov 06 2012

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..250

Index entries for linear recurrences with constant coefficients, signature (16,-15).

FORMULA

a(n) = (15^n - 1)/14.

a(n) = 15*a(n-1) + 1 with n>1, a(1)=1. - Vincenzo Librandi, Aug 03 2010

G.f.: x/((1-x)*(1-15*x)). - Bruno Berselli, Nov 07 2012

a(1)=1, a(2)=16; for n>2, a(n) = 16*a(n-1) - 15*a(n-2). - Harvey P. Dale, Jul 08 2013

a(n) = Sum_{i=0...n-1} 14^i*binomial(n,n-1-i). - Bruno Berselli, Nov 12 2015

E.g.f.: (1/14)*(exp(15*x) - exp(x)). - G. C. Greubel, Oct 17 2016

EXAMPLE

a(4) = 15^3+15^2+15^1+1 = 3375+225+15+1 = 3616.

For n=6, a(6) = 1*6 + 14*15 + 14^2*20 + 14^3*15 + 14^4*6 + 14^5*1 = 813616. - Bruno Berselli, Nov 12 2015

MATHEMATICA

Table[FromDigits[PadRight[{}, n, 1], 15], {n, 20}] (* or *) LinearRecurrence[{16, -15}, {1, 16}, 20] (* Harvey P. Dale, Jul 08 2013 *)

PROG

(Sage) [gaussian_binomial(n, 1, 15) for n in xrange(1, 15)] # Zerinvary Lajos, May 28 2009

(Sage) [(15^n-1)/14 for n in (1..30)] # Bruno Berselli, Nov 12 2015

(Maxima) A135518(n):=(15^n-1)/14$ makelist(A135518(n), n, 1, 30); /*  Martin Ettl, Nov 05 2012 */

(PARI) a(n)=(15^n-1)/14 \\ Charles R Greathouse IV, Sep 24 2015

CROSSREFS

Cf. A000225, A003462, A002450, A003463, A003464, A023000, A023001, A002452, A016123, A016125.

Cf. A001023, A135278.

Sequence in context: A204793 A173605 A175720 * A179092 A231020 A274856

Adjacent sequences:  A135515 A135516 A135517 * A135519 A135520 A135521

KEYWORD

nonn,easy

AUTHOR

Julien Peter Benney (jpbenney(AT)gmail.com), Feb 19 2008

STATUS

approved

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Last modified June 22 12:24 EDT 2017. Contains 288613 sequences.