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 A130485 a(n) = Sum_{k=0..n} (k mod 7) (Partial sums of A010876). 21
 0, 1, 3, 6, 10, 15, 21, 21, 22, 24, 27, 31, 36, 42, 42, 43, 45, 48, 52, 57, 63, 63, 64, 66, 69, 73, 78, 84, 84, 85, 87, 90, 94, 99, 105, 105, 106, 108, 111, 115, 120, 126, 126, 127, 129, 132, 136, 141, 147, 147, 148, 150, 153, 157, 162, 168, 168, 169, 171, 174, 178, 183 (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 7, 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 (1,0,0,0,0,0,1,-1). FORMULA a(n) = 21*floor(n/7) + A010876(n)*(A010876(n) + 1)/2. G.f.: (Sum_{k=1..6} k*x^k)/((1-x^7)*(1-x)). G.f.: x*(1 - 7*x^6 + 6*x^7)/((1-x^7)*(1-x)^3). MAPLE a:=n->add(chrem( [n, j], [1, 7] ), j=1..n):seq(a(n), n=1..70); # Zerinvary Lajos, Apr 07 2009 MATHEMATICA LinearRecurrence[{1, 0, 0, 0, 0, 0, 1, -1}, {0, 1, 3, 6, 10, 15, 21, 21}, 70] (* Harvey P. Dale, Jul 30 2017 *) PROG (PARI) concat(0, Vec((1-7*x^6+6*x^7)/(1-x^7)/(1-x)^3+O(x^70))) \\ Charles R Greathouse IV, Dec 22 2011 (Magma) I:=[0, 1, 3, 6, 10, 15, 21, 21]; [n le 8 select I[n] else Self(n-1) + Self(n-7) - Self(n-8): n in [1..71]]; // G. C. Greubel, Aug 31 2019 (Sage) def A130485_list(prec):     P. = PowerSeriesRing(ZZ, prec)     return P(x*(1-7*x^6+6*x^7)/((1-x^7)*(1-x)^3)).list() A130485_list(70) # G. C. Greubel, Aug 31 2019 (GAP) a:=[0, 1, 3, 6, 10, 15, 21, 21];; for n in [9..71] do a[n]:=a[n-1]+a[n-7]-a[n-8]; od; a; # G. C. Greubel, Aug 31 2019 CROSSREFS Cf. A010872, A010873, A010874, A010875, A010877, A130481, A130482, A130483, A130484. Sequence in context: A034175 A306698 A139131 * A115015 A231676 A056150 Adjacent sequences:  A130482 A130483 A130484 * A130486 A130487 A130488 KEYWORD nonn,easy AUTHOR Hieronymus Fischer, May 31 2007 STATUS approved

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Last modified November 26 08:23 EST 2022. Contains 358354 sequences. (Running on oeis4.)