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%I #28 Jul 28 2022 09:05:51
%S 0,1,3,6,10,15,21,28,36,45,45,46,48,51,55,60,66,73,81,90,90,91,93,96,
%T 100,105,111,118,126,135,135,136,138,141,145,150,156,163,171,180,180,
%U 181,183,186,190,195,201,208,216,225,225,226,228,231,235,240,246,253
%N a(n) = Sum_{k=0..n} (k mod 10) (Partial sums of A010879).
%C Let A be the Hessenberg n X n matrix defined by A[1,j] = j mod 10, A[i,i]:=1, A[i,i-1]=-1. Then, for n >= 1, a(n)=det(A). - _Milan Janjic_, Jan 24 2010
%H Shawn A. Broyles, <a href="/A130488/b130488.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,0,0,0,0,1,-1).
%F a(n) = 45*floor(n/10) + A010879(n)*(A010879(n) + 1)/2.
%F G.f.: (Sum_{k=1..9} k*x^k)/((1-x^10)*(1-x)).
%F G.f.: x*(1 - 10*x^9 + 9*x^10)/((1-x^10)*(1-x)^3).
%p seq(coeff(series(x*(1-10*x^9+9*x^10)/((1-x^10)*(1-x)^3), x, n+1), x, n), n = 0..60); # _G. C. Greubel_, Aug 31 2019
%t LinearRecurrence[{1,0,0,0,0,0,0,0,0,1,-1}, {0,1,3,6,10,15,21,28,36,45, 45}, 60] (* _G. C. Greubel_, Aug 31 2019 *)
%o (PARI) a(n) = sum(k=0, n, k % 10); \\ _Michel Marcus_, Apr 28 2018
%o (Magma) I:=[0,1,3,6,10,15,21,28,36,45,45]; [n le 11 select I[n] else Self(n-1) + Self(n-10) - Self(n-11): n in [1..61]]; // _G. C. Greubel_, Aug 31 2019
%o (Sage)
%o def A130488_list(prec):
%o P.<x> = PowerSeriesRing(ZZ, prec)
%o return P(x*(1-10*x^9+9*x^10)/((1-x^10)*(1-x)^3)).list()
%o A130488_list(60) # _G. C. Greubel_, Aug 31 2019
%o (GAP) a:=[0,1,3,6,10,15,21,28,36,45,45];; for n in [12..61] do a[n]:=a[n-1]+a[n-10]-a[n-11]; od; a; # _G. C. Greubel_, Aug 31 2019
%o (Python)
%o def A130488(n):
%o a, b = divmod(n,10)
%o return 45*a+(b*(b+1)>>1) # _Chai Wah Wu_, Jul 27 2022
%Y Cf. A010872, A010873, A010874, A010875, A010876, A010877, A010878, A130481, A130482, A130483, A130484, A130485, A130486, A130487.
%K nonn
%O 0,3
%A _Hieronymus Fischer_, May 31 2007
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