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%I #49 Sep 08 2022 08:45:07
%S 2,7,29,133,641,3157,15689,78253,390881,1953637,9766649,48830173,
%T 244144721,1220711317,6103532009,30517610893,152587956161,
%U 762939584197,3814697527769,19073486852413,95367432689201,476837160300277
%N a(n) = 2^n + 5^n.
%C Digital root of a(n) is A010697(n). - _Peter M. Chema_, Oct 24 2016
%D Miller, Steven J., ed. Benford's Law: Theory and Applications. Princeton University Press, 2015. See page 14.
%H Vincenzo Librandi, <a href="/A074600/b074600.txt">Table of n, a(n) for n = 0..200</a>
%H D. Suprijanto, I. W. Suwarno, <a href="http://dx.doi.org/10.12988/ams.2014.4139">Observation on Sums of Powers of Integers Divisible by 3k-1</a>, Applied Mathematical Sciences, Vol. 8, 2014, no. 45, pp. 2211-2217.
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (7,-10).
%F a(n) = 5*a(n-1)-3*2^(n-1) = 7*a(n-1)- 10*a(n-2). [Corrected by _Zak Seidov_, Oct 24 2009]
%F G.f.: 1/(1-2*x)+1/(1-5*x). E.g.f.: e^(2*x)+e^(5*x). - _Mohammad K. Azarian_, Jan 02 2009
%t Table[2^n + 5^n, {n, 0, 25}]
%t LinearRecurrence[{7,-10},{2,7},30] (* _Harvey P. Dale_, May 09 2019 *)
%o (Magma) [2^n + 5^n: n in [0..35]]; // _Vincenzo Librandi_, Apr 30 2011
%o (PARI) a(n)=2^n+5^n \\ _Charles R Greathouse IV_, Sep 24 2015
%Y Cf. A000051, A034472, A052539, A034474, A062394, A034491, A062395, A062396, A007689, A063376, A063481, A074601-A074624, A010697, A094475, A337429.
%K easy,nonn
%O 0,1
%A _Robert G. Wilson v_, Aug 25 2002
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