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 A130482 a(n) = Sum_{k=0..n} (k mod 4) (Partial sums of A010873). 28
 0, 1, 3, 6, 6, 7, 9, 12, 12, 13, 15, 18, 18, 19, 21, 24, 24, 25, 27, 30, 30, 31, 33, 36, 36, 37, 39, 42, 42, 43, 45, 48, 48, 49, 51, 54, 54, 55, 57, 60, 60, 61, 63, 66, 66, 67, 69, 72, 72, 73, 75, 78, 78, 79, 81, 84, 84, 85, 87, 90, 90, 91, 93, 96, 96, 97, 99, 102, 102, 103, 105 (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 4, A[i,i]:=1, A[i,i-1]=-1. Then, for n>=1, a(n)=det(A). - Milan Janjic, Jan 24 2010 LINKS Colin Barker, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1). FORMULA a(n) = 6*floor(n/4) + A010873(n)*(A010873(n)+1)/2. G.f.: x*(1 + 2*x + 3*x^2)/((1-x^4)*(1-x)). a(n) = (1 - (-1)^n - (2*i)*(-i)^n + (2*i)*i^n + 6*n) / 4 where i = sqrt(-1). - Colin Barker, Oct 15 2015 a(n) = 3*n/2 + (n mod 2)* ( (n-1) mod 4 ) - (n mod 2)/2. - Ammar Khatab, Aug 27 2020 E.g.f.: (3*x*exp(x) - 2*sin(x) + sinh(x))/2. - Stefano Spezia, Apr 22 2021 Sum_{n>=1} (-1)^(n+1)/a(n) = Pi/(4*sqrt(3)) + log(3)/4. - Amiram Eldar, Sep 17 2022 MAPLE a:=n->add(chrem( [n, j], [1, 4] ), j=1..n):seq(a(n), n=0..70); # Zerinvary Lajos, Apr 07 2009 MATHEMATICA Table[(6*n +(1-(-1)^n)*(1+2*I^(n+1)))/4, {n, 0, 70}] (* G. C. Greubel, Aug 31 2019 *) PROG (PARI) a(n) = (1 - (-1)^n - (2*I)*(-I)^n + (2*I)*I^n + 6*n) / 4 \\ Colin Barker, Oct 15 2015 (Magma) I:=[0, 1, 3, 6, 6]; [n le 5 select I[n] else Self(n-1) + Self(n-4) - Self(n-5): n in [1..71]]; // G. C. Greubel, Aug 31 2019 (Sage) def A130482_list(prec):     P. = PowerSeriesRing(ZZ, prec)     return P(x*(1+2*x+3*x^2)/((1-x^4)*(1-x))).list() A130482_list(70) # G. C. Greubel, Aug 31 2019 (GAP) a:=[0, 1, 3, 6, 6];; for n in [6..71] do a[n]:=a[n-1]+a[n-4]-a[n-5]; od; a; # G. C. Greubel, Aug 31 2019 CROSSREFS Cf. A010872, A010874, A010875, A010876, A010877. A130481, A130483, A130484, A130485. Sequence in context: A153035 A296216 A072910 * A239318 A177783 A228945 Adjacent sequences:  A130479 A130480 A130481 * A130483 A130484 A130485 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.)