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%I #28 Oct 21 2022 22:08:26
%S 0,1,3,6,10,15,21,28,36,36,37,39,42,46,51,57,64,72,72,73,75,78,82,87,
%T 93,100,108,108,109,111,114,118,123,129,136,144,144,145,147,150,154,
%U 159,165,172,180,180,181,183,186,190,195,201,208,216,216,217,219,222,226
%N a(n) = Sum_{k=0..n} (k mod 9) (Partial sums of A010878).
%C Let A be the Hessenberg n X n matrix defined by A[1,j]=j mod 9, 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="/A130487/b130487.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,0,0,0,1,-1).
%F a(n) = 36*floor(n/9) + A010878(n)*(A010878(n) + 1)/2.
%F G.f.: (Sum_{k=1..8} k*x^k)/((1-x^9)*(1-x)).
%F G.f.: x*(1 - 9*x^8 + 8*x^9)/((1-x^9)*(1-x)^3).
%p seq(coeff(series(x*(1-9*x^8+8*x^9)/((1-x^9)*(1-x)^3), x, n+1), x, n), n = 0 .. 70); # _G. C. Greubel_, Aug 31 2019
%t Accumulate[PadRight[{},120,Range[0,8]]] (* _Harvey P. Dale_, Dec 19 2018 *)
%t Accumulate[Mod[Range[0,100],9]] (* _Harvey P. Dale_, Oct 16 2021 *)
%o (PARI) a(n) = sum(k=0, n, k % 9); \\ _Michel Marcus_, Apr 28 2018
%o (Magma) I:=[0,1,3,6,10,15,21,28,36,36]; [n le 10 select I[n] else Self(n-1) + Self(n-9) - Self(n-10): n in [1..71]]; // _G. C. Greubel_, Aug 31 2019
%o (Sage)
%o def A130487_list(prec):
%o P.<x> = PowerSeriesRing(ZZ, prec)
%o return P(x*(1-9*x^8+8*x^9)/((1-x^9)*(1-x)^3)).list()
%o A130487_list(70) # _G. C. Greubel_, Aug 31 2019
%o (GAP) a:=[0,1,3,6,10,15,21,28,36,36];; for n in [11..71] do a[n]:=a[n-1]+a[n-9]-a[n-10]; od; a; # _G. C. Greubel_, Aug 31 2019
%Y Cf. A010872, A010873, A010874, A010875, A010876, A010877, A130481, A130482, A130483, A130484, A130485, A130486.
%K nonn,easy
%O 0,3
%A _Hieronymus Fischer_, May 31 2007
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