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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
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.<x> = 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
Sequence in context: A337602 A360946 A032570 * A115012 A200723 A135738
KEYWORD
nonn,easy
AUTHOR
Hieronymus Fischer, May 29 2007
STATUS
approved

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Last modified March 29 08:01 EDT 2024. Contains 371265 sequences. (Running on oeis4.)