%I #19 Sep 08 2022 08:45:00

%S 45,145,245,345,445,545,645,745,845,945,1045,1145,1245,1345,1445,1545,

%T 1645,1745,1845,1945,2045,2145,2245,2345,2445,2545,2645,2745,2845,

%U 2945,3045,3145,3245,3345,3445,3545,3645,3745,3845,3945,4045,4145,4245,4345

%N Sum of numbers in range 10*n to 10*n+9.

%H Harvey P. Dale, <a href="/A053743/b053743.txt">Table of n, a(n) for n = 0..1000</a>

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

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).

%F a(n) = 100*n + 45.

%F From _Colin Barker_, Jun 26 2012: (Start)

%F a(n) = 2*a(n-1) - a(n-2).

%F G.f.: 5*(9+11*x)/(1-x)^2. (End)

%F E.g.f.: 5*(9 + 20*x)*exp(x). - _G. C. Greubel_, Sep 06 2019

%e 45 = sum of 0, 1, 2, 3, 4, 5, 6, 7, 8, 9;

%e 145 = sum of 10, 11, 12, 13, 14, 15, 16, 17, 18, 19.

%p seq(5*(20*n+9), n=0..50); # _G. C. Greubel_, Sep 06 2019

%t LinearRecurrence[{2,-1},{45,145},50] (* or *) 100*Range[50]-55 (* _Harvey P. Dale_, Feb 03 2019 *)

%o (PARI) vector(50, n, 5*(20*n -11)) \\ _G. C. Greubel_, Sep 06 2019

%o (Magma) [5*(20*n+9): n in [0..50]]; // _G. C. Greubel_, Sep 06 2019

%o (Sage) [5*(20*n+9) for n in (0..50)] # _G. C. Greubel_, Sep 06 2019

%o (GAP) List([0..50], n-> 5*(20*n+9)); # _G. C. Greubel_, Sep 06 2019

%Y Cf. A053741, A053742.

%K nonn,easy

%O 0,1

%A _Odimar Fabeny_, Feb 13 2000

%E More terms from _James A. Sellers_, Feb 22 2000