OFFSET
0,3
COMMENTS
Let A be the Hessenberg n X n matrix defined by A[1,j] = j mod 8, 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 (1,0,0,0,0,0,0,1,-1).
FORMULA
MAPLE
seq(coeff(series(x*(1-8*x^7+7*x^8)/((1-x^8)*(1-x)^3), x, n+1), x, n), n = 0 .. 40); # G. C. Greubel, Aug 31 2019
MATHEMATICA
Array[28 Floor[#1/8] + #2 (#2 + 1)/2 & @@ {#, Mod[#, 8]} &, 61, 0] (* Michael De Vlieger, Apr 28 2018 *)
Accumulate[PadRight[{}, 100, Range[0, 7]]] (* Harvey P. Dale, Dec 21 2018 *)
PROG
(PARI) a(n) = sum(k=0, n, k % 8); \\ Michel Marcus, Apr 28 2018
(Magma) I:=[0, 1, 3, 6, 10, 15, 21, 28, 28]; [n le 9 select I[n] else Self(n-1) + Self(n-8) - Self(n-9): n in [1..71]]; // G. C. Greubel, Aug 31 2019
(Sage)
def A130486_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P(x*(1-8*x^7+7*x^8)/((1-x^8)*(1-x)^3)).list()
A130486_list(70) # G. C. Greubel, Aug 31 2019
(GAP) a:=[0, 1, 3, 6, 10, 15, 21, 28, 28];; for n in [10..71] do a[n]:=a[n-1]+a[n-8]-a[n-9]; od; a; # G. C. Greubel, Aug 31 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Hieronymus Fischer, May 31 2007
STATUS
approved