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%I #33 Apr 08 2022 22:38:22
%S 0,1,65,4161,266305,17043521,1090785345,69810262081,4467856773185,
%T 285942833483841,18300341342965825,1171221845949812801,
%U 74958198140788019265,4797324681010433232961,307028779584667726909505,19649841893418734522208321,1257589881178799009421332545
%N a(n) = (64^n - 1)/63.
%C Partial sums of powers of 64 (A089357), a.k.a. q-numbers for q=64.
%H Vincenzo Librandi, <a href="/A133853/b133853.txt">Table of n, a(n) for n = 0..500</a>
%H Quynh Nguyen, Jean Pedersen, and Hien T. Vu, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL19/Pedersen/pedersen2.html">New Integer Sequences Arising From 3-Period Folding Numbers</a>, Vol. 19 (2016), Article 16.3.1. See Table 1.
%H <a href="/index/Par#partial">Index entries related to partial sums</a>
%H <a href="/index/Q#q-numbers">Index entries related to q-numbers</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (65,-64).
%F From _Wolfdieter Lang_, Apr 08 2022: (Start)
%F a(n) = Sum_{j=0..n-1} 2^(6*j). See the comment.
%F G.f.: x/((1 - 64*x)*(1 - x)).
%F E.g.f.: exp(x)*(exp(63*x) - 1)/63. (End)
%t LinearRecurrence[{65,-64},{0,1},20] (* _Harvey P. Dale_, Aug 20 2017 *)
%o (Magma) [(64^n-1)/63: n in [0..20]]; // _Vincenzo Librandi_, Aug 10 2011
%o (PARI) A133853(n)=64^n\63
%o (Maxima) makelist((64^n-1)/63, n, 0, 20); /* _Martin Ettl_, Nov 12 2012 */
%Y Cf. A000364.
%Y Cf. similar sequences of the form (k^n-1)/(k-1) listed in A269025.
%K nonn,easy
%O 0,3
%A _Paul Curtz_, Jan 07 2008
%E a(6)-a(15) from _Vincenzo Librandi_, Aug 10 2011
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