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Sum of 5 consecutive powers of 3, starting with a power of 9.
2

%I #18 Sep 08 2022 08:45:25

%S 121,1089,9801,88209,793881,7144929,64304361,578739249,5208653241,

%T 46877879169,421900912521,3797108212689,34173973914201,

%U 307565765227809,2768091887050281,24912826983452529,224215442851072761,2017938985659654849,18161450870936893641

%N Sum of 5 consecutive powers of 3, starting with a power of 9.

%C Always a square.

%H Vincenzo Librandi, <a href="/A120353/b120353.txt">Table of n, a(n) for n = 1..300</a>

%H Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>

%H <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (9).

%F a(n) = 121*3^(2n-2).

%e a(2) = 3^2 + 3^3 + 3^4 + 3^5 + 3^6 = 121*(3^2) = 1089.

%t Total/@Select[Partition[3^Range[0,60],5,1],IntegerQ[Log[9, First[#]]]&] (* or *) Table[121 3^(2n-2),{n,30}] (* _Harvey P. Dale_, May 03 2011 *)

%o (Magma) [121*3^(2*n-2): n in [1..30]]; // _Vincenzo Librandi_, Jun 10 2011

%o (PARI) a(n)=121*9^(n-1) \\ _Charles R Greathouse IV_, Jul 11 2016

%K nonn,easy

%O 1,1

%A _Anton Joha_, Jun 25 2006

%E Corrected and extended by _Harvey P. Dale_, May 03 2011