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%I #32 Sep 08 2022 08:45:02
%S 1,7,37,187,937,4687,23437,117187,585937,2929687,14648437,73242187,
%T 366210937,1831054687,9155273437,45776367187,228881835937,
%U 1144409179687,5722045898437,28610229492187,143051147460937,715255737304687,3576278686523437,17881393432617187
%N a(n) = (3 * 5^n - 1)/2.
%C Sum of n-th row of triangle of powers of 5: 1; 1 5 1; 1 5 25 5 1 ; 1 5 25 125 25 5 1; ... - _Philippe Deléham_, Feb 23 2014
%H Vincenzo Librandi, <a href="/A057651/b057651.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (6,-5).
%F G.f.: (1+x)/(1 - 6*x + 5*x^2).
%F a(0)=1, a(n) = 5*a(n-1) + 2; a(n) = a(n-1) + 6*(5^(n-1)). - _Amarnath Murthy_, May 27 2001
%F a(n) = 6*a(n-1) - 5*a(n-2), n > 1. - _Vincenzo Librandi_, Oct 30 2011
%F a(n) = Sum_{k=0..n} A112468(n,k)*6^k. - _Philippe Deléham_, Feb 23 2014
%e a(0) = 1;
%e a(1) = 1 + 5 + 1 = 7;
%e a(2) = 1 + 5 + 25 + 5 + 1 = 37;
%e a(3) = 1 + 5 + 25 + 125 + 25 + 5 + 1 = 187; etc. - _Philippe Deléham_, Feb 23 2014
%e G.f. = 1 + 7*x + 37*x^2 + 187*x^3 + 937*x^4 + 4687*x^5 + 23437*x^6 + ...
%p G.f=(1+x)/(1-5*x)/(1-x): gser:=series(g, x=0, 43): seq(coeff(gser, x, n), n=0..30); # _Zerinvary Lajos_, Jan 11 2009
%t Table[(3*5^n-1)/2,{n,0,30}] (* _Vladimir Joseph Stephan Orlovsky_, Jan 29 2012 *)
%o (Magma) [(3*5^n-1)/2: n in [0..30]]; // _Vincenzo Librandi_, Oct 30 2011
%o (PARI) a(n)=3*5^n\2 \\ _Charles R Greathouse IV_, Dec 22 2011
%Y Cf. A024049, A081655.
%Y Cf. A020989, A061801, A112468, A112739.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_, Oct 13 2000
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