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 A130483 a(n) = Sum_{k=0..n} (k mod 5) (Partial sums of A010874). 26
 0, 1, 3, 6, 10, 10, 11, 13, 16, 20, 20, 21, 23, 26, 30, 30, 31, 33, 36, 40, 40, 41, 43, 46, 50, 50, 51, 53, 56, 60, 60, 61, 63, 66, 70, 70, 71, 73, 76, 80, 80, 81, 83, 86, 90, 90, 91, 93, 96, 100, 100, 101, 103, 106, 110, 110, 111, 113, 116, 120, 120, 121, 123, 126, 130, 130 (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 5, 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 (1,0,0,0,1,-1). FORMULA a(n) = 10*floor(n/5) + A010874(n)*(A010874(n)+1)/2. G.f.: x*(1 + 2*x + 3*x^2 + 4*x^3)/((1-x^5)*(1-x)). From Wesley Ivan Hurt, Jul 23 2016: (Start) a(n) = a(n-5) - a(n-6) for n>5; a(n) = a(n-5) + 10 for n>4. a(n) = 10 + Sum_{k=1..4} k*floor((n-k)/5). (End) a(n) = ((n mod 5)^2 - 3*(n mod 5) + 4*n)/2. - Ammar Khatab, Aug 13 2020 MAPLE seq(coeff(series(x*(1+2*x+3*x^2+4*x^3)/((1-x^5)*(1-x)), x, n+1), x, n), n = 0..70); # G. C. Greubel, Aug 31 2019 MATHEMATICA Accumulate[Mod[Range[0, 70], 5]] (* or *) Accumulate[PadRight[{}, 70, {0, 1, 2, 3, 4}]] (* Harvey P. Dale, Nov 11 2016 *) PROG (PARI) a(n) = sum(k=0, n, k % 5); \\ Michel Marcus, Apr 28 2018 (Magma) I:=[0, 1, 3, 6, 10, 10]; [n le 6 select I[n] else Self(n-1) + Self(n-5) - Self(n-6): n in [1..71]]; // G. C. Greubel, Aug 31 2019 (Sage) def A130483_list(prec):     P. = PowerSeriesRing(ZZ, prec)     return P(x*(1+2*x+3*x^2+4*x^3)/((1-x^5)*(1-x))).list() A130483_list(70) # G. C. Greubel, Aug 31 2019 (GAP) a:=[0, 1, 3, 6, 10, 10];; for n in [7..71] do a[n]:=a[n-1]+a[n-5]-a[n-6]; od; a; # G. C. Greubel, Aug 31 2019 CROSSREFS Cf. A010872, A010873, A010875, A010876, A010877, A130481, A130482, A130484, A130485. Sequence in context: A198456 A337602 A032570 * A115012 A200723 A135738 Adjacent sequences:  A130480 A130481 A130482 * A130484 A130485 A130486 KEYWORD nonn,easy AUTHOR Hieronymus Fischer, May 29 2007 STATUS approved

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Last modified November 26 05:48 EST 2022. Contains 358353 sequences. (Running on oeis4.)