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%I #29 Sep 06 2017 20:12:43
%S 5,30,80,155,255,380,530,705,905,1130,1380,1655,1955,2280,2630,3005,
%T 3405,3830,4280,4755,5255,5780,6330,6905,7505,8130,8780,9455,10155,
%U 10880,11630,12405,13205,14030,14880,15755,16655,17580,18530
%N 5 times centered pentagonal numbers: 5*(5*n^2 + 5*n + 2)/2.
%H Ivan Panchenko, <a href="/A164015/b164015.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F a(n) = 5*A005891(n).
%F a(n) = a(n-1) + 25*n (with a(0)=5). - _Vincenzo Librandi_, Nov 30 2010
%F a(0)=5, a(1)=30, a(2)=80, a(n) = 3*a(n-1)-3*a(n-2)+a(n-3). - _Harvey P. Dale_, Oct 08 2011
%F G.f.: (5*(x*(x+3)+1))/(1-x)^3. - _Harvey P. Dale_, Oct 08 2011
%F E.g.f.: (5/2)*(2 + 10*x + 5*x^2)*exp(x). - _G. C. Greubel_, Sep 06 2017
%t Table[5(5n^2+5n+2)/2,{n,0,40}] (* or *) LinearRecurrence[{3,-3,1},{5,30,80},40] (* _Harvey P. Dale_, Oct 08 2011 *)
%o (PARI) a(n)=25*n*(n+1)/2+5 \\ _Charles R Greathouse IV_, Jul 17 2011
%Y Cf. A005891, A152734, A164013, A108099, A164016.
%K easy,nonn
%O 0,1
%A _Omar E. Pol_, Nov 07 2009
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