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 A130484 a(n) = Sum_{k=0..n} (k mod 6) (Partial sums of A010875). 22
 0, 1, 3, 6, 10, 15, 15, 16, 18, 21, 25, 30, 30, 31, 33, 36, 40, 45, 45, 46, 48, 51, 55, 60, 60, 61, 63, 66, 70, 75, 75, 76, 78, 81, 85, 90, 90, 91, 93, 96, 100, 105, 105, 106, 108, 111, 115, 120, 120, 121, 123, 126, 130, 135, 135, 136, 138, 141, 145, 150, 150, 151, 153 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS 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 LINKS Shawn A. Broyles, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,1,-1). FORMULA a(n) = 15*floor(n/6) + A010875(n)*(A010875(n) + 1)/2. 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). MAPLE 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 MATHEMATICA Accumulate[Mod[Range[0, 70], 6]] (* or *) Accumulate[PadRight[ {}, 70, Range[0, 5]]] (* Harvey P. Dale, Jul 12 2016 *) PROG (PARI) a(n) = sum(k=0, n, k % 6); \\ Michel Marcus, Apr 28 2018 (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 (Sage) def A130484_list(prec):     P. = PowerSeriesRing(ZZ, prec)     return P(x*(1-6*x^5+5*x^6)/((1-x^6)*(1-x)^3)).list() A130484_list(70) # G. C. Greubel, Aug 31 2019 (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 CROSSREFS Cf. A010872, A010873, A010874, A010876, A010877, A130481, A130482, A130483, A130485. Sequence in context: A105333 A126234 A259604 * A074374 A109804 A231672 Adjacent sequences:  A130481 A130482 A130483 * A130485 A130486 A130487 KEYWORD nonn AUTHOR Hieronymus Fischer, May 31 2007 STATUS approved

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Last modified October 16 09:29 EDT 2019. Contains 328056 sequences. (Running on oeis4.)