The OEIS is supported by the many generous donors to the OEIS Foundation.

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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 (PARI) a(n)=n\6*15 + binomial(n%6+1, 2) \\ Charles R Greathouse IV, Jan 24 2022 (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,easy AUTHOR Hieronymus Fischer, May 31 2007 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified November 26 07:48 EST 2022. Contains 358353 sequences. (Running on oeis4.)