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A130483 a(n) = Sum_{k=0..n} (k mod 5) (Partial sums of A010874). 25
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

Table of n, a(n) for n=0..65.

Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,1,-1).

FORMULA

a(n) = 10*floor(n/5) + A010874(n)*(A010874(n)+1)/2.

G.f.: (4*x^4 + 3*x^3 + 2*x^2 + x)/((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)

MAPLE

a:=n->add(chrem( [n, j], [1, 5] ), j=1..n):seq(a(n), n=0..65); # Zerinvary Lajos, Apr 07 2009

MATHEMATICA

f[n_]:=Mod[n, 5]; s=0; lst={}; Do[AppendTo[lst, s+=f[n]], {n, 0, 5!}]; lst (* Vladimir Joseph Stephan Orlovsky, Feb 07 2010 *)

Accumulate[Mod[Range[0, 70], 5]] (* or *) Accumulate[PadRight[{}, 70, {0, 1, 2, 3, 4}]] (* Harvey P. Dale, Nov 11 2016 *)

CROSSREFS

Cf. A010872, A010873, A010875, A010876, A010877, A130481, A130482, A130484, A130485.

Sequence in context: A198467 A198456 A032570 * A115012 A200723 A135738

Adjacent sequences:  A130480 A130481 A130482 * A130484 A130485 A130486

KEYWORD

nonn,easy

AUTHOR

Hieronymus Fischer, May 29 2007

STATUS

approved

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Last modified November 18 14:28 EST 2017. Contains 294894 sequences.