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%I #22 Apr 16 2024 10:26:13
%S 10,55,100,145,190,235,280,325,370,415,460,505,550,595,640,685,730,
%T 775,820,865,910,955,1000,1045,1090,1135,1180,1225,1270,1315,1360,
%U 1405,1450,1495,1540,1585,1630,1675,1720,1765,1810,1855,1900
%N a(n) = 45*n + 10.
%C Numbers of the 10th column of positive numbers in the square array of nonnegative and polygonal numbers A139600.
%H Vincenzo Librandi, <a href="/A139610/b139610.txt">Table of n, a(n) for n = 0..5000</a>
%H <a href="/index/Pol#polygonal_numbers">Index to sequences related to polygonal numbers</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).
%F a(n) = A057145(n+2,10).
%F G.f.: 5*(2+7*x)/(x-1)^2. - _R. J. Mathar_, Jul 28 2016
%F From _Elmo R. Oliveira_, Apr 16 2024: (Start)
%F E.g.f.: 5*exp(x)*(2 + 9*x).
%F a(n) = 5*A017185(n) = 5*(A062708(n+1) - A062708(n)).
%F a(n) = 2*a(n-1) - a(n-2) for n >= 2. (End)
%t 45*Range[0,50]+10 (* or *) LinearRecurrence[{2,-1},{10,55},50] (* _Harvey P. Dale_, Dec 27 2021 *)
%o (Magma) [5*(9*n + 2): n in [0..60]]; // _Vincenzo Librandi_, Jul 23 2011
%o (PARI) a(n)=45*n+10 \\ _Charles R Greathouse IV_, Oct 05 2011
%Y Cf. A017185, A057145, A062708, A139600.
%K easy,nonn,changed
%O 0,1
%A _Omar E. Pol_, Apr 27 2008
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