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A130484 a(n) = Sum_{k=0..n} (k mod 6) (Partial sums of A010875).

%I A130484 #34 Sep 08 2022 08:45:30
%S A130484 0,1,3,6,10,15,15,16,18,21,25,30,30,31,33,36,40,45,45,46,48,51,55,60,
%T A130484 60,61,63,66,70,75,75,76,78,81,85,90,90,91,93,96,100,105,105,106,108,
%U A130484 111,115,120,120,121,123,126,130,135,135,136,138,141,145,150,150,151,153
%N A130484 a(n) = Sum_{k=0..n} (k mod 6) (Partial sums of A010875).
%C A130484 Let A be the Hessenberg n X n matrix defined by A[1,j] = j mod 6, A[i,i]=1, A[i,i-1]=-1. Then, for n >= 1, a(n)=det(A). - _Milan Janjic_, Jan 24 2010
%H A130484 Shawn A. Broyles, <a href="/A130484/b130484.txt">Table of n, a(n) for n = 0..1000</a>
%H A130484 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,1,-1).
%F A130484 a(n) = 15*floor(n/6) + A010875(n)*(A010875(n) + 1)/2.
%F A130484 G.f.: (Sum_{k=1..5} k*x^k)/((1-x^6)*(1-x)) = x*(1 - 6*x^5 + 5*x^6)/((1-x^6)*(1-x)^3).
%p A130484 seq(coeff(series(x*(1-6*x^5+5*x^6)/((1-x^6)*(1-x)^3), x, n+1), x, n), n = 0 .. 70); # _G. C. Greubel_, Aug 31 2019
%t A130484 Accumulate[Mod[Range[0,70],6]] (* or *) Accumulate[PadRight[ {},70, Range[0,5]]] (* _Harvey P. Dale_, Jul 12 2016 *)
%o A130484 (PARI) a(n) = sum(k=0, n, k % 6); \\ _Michel Marcus_, Apr 28 2018
%o A130484 (PARI) a(n)=n\6*15 + binomial(n%6+1,2) \\ _Charles R Greathouse IV_, Jan 24 2022
%o A130484 (Magma) I:=[0,1,3,6,10,15,15]; [n le 7 select I[n] else Self(n-1) + Self(n-6) - Self(n-7): n in [1..71]]; // _G. C. Greubel_, Aug 31 2019
%o A130484 (Sage)
%o A130484 def A130484_list(prec):
%o A130484     P.<x> = PowerSeriesRing(ZZ, prec)
%o A130484     return P(x*(1-6*x^5+5*x^6)/((1-x^6)*(1-x)^3)).list()
%o A130484 A130484_list(70) # _G. C. Greubel_, Aug 31 2019
%o A130484 (GAP) a:=[0,1,3,6,10,15,15];; for n in [8..71] do a[n]:=a[n-1]+a[n-6]-a[n-7]; od; a; # _G. C. Greubel_, Aug 31 2019
%Y A130484 Cf. A010872, A010873, A010874, A010876, A010877, A130481, A130482, A130483, A130485.
%K A130484 nonn,easy
%O A130484 0,3
%A A130484 _Hieronymus Fischer_, May 31 2007