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A091045 Partial sums of powers of 17 (A001026). 37
1, 18, 307, 5220, 88741, 1508598, 25646167, 435984840, 7411742281, 125999618778, 2141993519227, 36413889826860, 619036127056621, 10523614159962558, 178901440719363487, 3041324492229179280, 51702516367896047761 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

17^a(n) is highest power of 17 dividing (17^n)!.

Let A be the Hessenberg matrix of order n, defined by: A[1,j]=1, A[i,i]:=17, (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

LINKS

Table of n, a(n) for n=1..17.

FORMULA

a(n)= sum(17^k, k=0..n-1) = (17^n-1)/16.

G.f.: x/((1-17*x)*(1-x))= (1/(1-17*x) - 1/(1-x))/16.

For analogs with primes 2, 3, 5, 7, 11, 13, ... see: A000225, A003462, A003463, A023000, A016123, A091030, ...

a(n)=17*a(n-1)+1 (with a(1)=1). - Vincenzo Librandi, Nov 16 2010

MATHEMATICA

Table[17^n, {n, 0, 16}] // Accumulate (* Jean-Fran├žois Alcover, Jul 05 2013 *)

PROG

(Sage) [gaussian_binomial(n, 1, 17) for n in xrange(1, 18)] # Zerinvary Lajos, May 28 2009

(Maxima) A091045(n):=sum(17^k, k, 0, n)$ makelist(A091045(n), n, 0, 30); /* Martin Ettl, Nov 05 2012 */

CROSSREFS

Sequence in context: A170651 A170699 A170737 * A179121 A226298 A208537

Adjacent sequences:  A091042 A091043 A091044 * A091046 A091047 A091048

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang, Jan 23 2004

STATUS

approved

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Last modified July 27 04:25 EDT 2017. Contains 289841 sequences.