A064108 a(n) = (20^n - 1)/19.
0, 1, 21, 421, 8421, 168421, 3368421, 67368421, 1347368421, 26947368421, 538947368421, 10778947368421, 215578947368421, 4311578947368421, 86231578947368421, 1724631578947368421, 34492631578947368421, 689852631578947368421, 13797052631578947368421, 275941052631578947368421
Offset: 0
Examples
From _N. J. A. Sloane_, Nov 04 2014: Can also be obtained by writing powers of 2 in a staggered array and adding them (cf. A249604). For example, a(9) is: ..........1 .........2 ........4 .......8 .....16 ....32 ...64 .128 256 ----------- 26947368421
Links
- M. F. Hasler, Table of n, a(n) for n = 0..100
- Kival Ngaokrajang, Illustration of initial terms
- Index entries related to partial sums
- Index entries related to q-numbers
- Index entries for linear recurrences with constant coefficients, signature (21,-20).
Crossrefs
Programs
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Maple
a:=n->sum(20^(n-j), j=0..n): seq(a(n), n=0..15); # Zerinvary Lajos, Feb 11 2007
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Mathematica
(20^Range[20]-1)/19 (* or *) NestList[20#+1&,1,20] (* Harvey P. Dale, Oct 04 2012 *)
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Maxima
A064108(n):=(20^n-1)/19$ makelist(A064108(n),n,1,30); /* Martin Ettl, Nov 05 2012 */
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PARI
for (n=0, 100, write("b064108.txt", n, " ", (20^n - 1)/19)) \\ Harry J. Smith, Sep 07 2009 -
PARI
A064108(n)=20^n\19 \\ M. F. Hasler, Nov 04 2012
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Sage
[gaussian_binomial(n,1,20) for n in range(1,17)] # Zerinvary Lajos, May 29 2009
Formula
a(n) = 20*a(n-1) + 1, with a(0)=0. - Vincenzo Librandi, Aug 07 2010
a(0)=0, a(1)=1, a(n) = 21*a(n-1) - 20*a(n-2). - Harvey P. Dale, Oct 04 2012
a(n) = floor(20^n/19). - M. F. Hasler, Nov 04 2012
G.f.: x/((1 - x)*(1 - 20*x)). - Bruno Berselli, Nov 06 2012
E.g.f.: exp(x)*(exp(19*x) - 1)/19. - Stefano Spezia, Mar 23 2023
Extensions
Edited and extended to offset 0 by M. F. Hasler, Nov 04 2012
Comments