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A130481 a(n) = Sum_{k=0..n} (k mod 3) (i.e., partial sums of A010872). 30
0, 1, 3, 3, 4, 6, 6, 7, 9, 9, 10, 12, 12, 13, 15, 15, 16, 18, 18, 19, 21, 21, 22, 24, 24, 25, 27, 27, 28, 30, 30, 31, 33, 33, 34, 36, 36, 37, 39, 39, 40, 42, 42, 43, 45, 45, 46, 48, 48, 49, 51, 51, 52, 54, 54, 55, 57, 57, 58, 60, 60, 61, 63, 63, 64, 66, 66, 67, 69, 69, 70, 72, 72 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Essentially the same as A092200. - R. J. Mathar, Jun 13 2008

Let A be the Hessenberg n X n matrix defined by: A[1,j]=j mod 3, A[i,i]:=1, A[i,i-1]=-1. Then, for n>=1, a(n)=det(A). - Milan Janjic, Jan 24 2010

2-adic valuation of A104537(n+1). - Gerry Martens, Jul 14 2015

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

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

FORMULA

a(n) = 3*floor(n/3)+A010872(n)*(A010872(n)+1)/2.

G.f.: g(x)=(2x^2+x)/((1-x^3)(1-x)).

a(n) = n+1-(Fibonacci(n+1) mod 2). - Gary Detlefs, Mar 13 2011

a(n) = [(n+1)/3]+[2(n+1)/3], where []=floor. - Clark Kimberling, May 28 2010

a(n) = n when n+1 is not a multiple of 3, and a(n) = n+1 when n+1 is a multiple of 3. - Dennis P. Walsh, Aug 06 2012

a(n) = n+1-sign((n+1) mod 3). - Wesley Ivan Hurt, Sep 25 2017

a(n) = n+(1-cos(2*(n+2)*Pi/3))/3+sin(2*(n+2)*Pi/3)/sqrt(3). - Wesley Ivan Hurt, Sep 27 2017

MAPLE

a:=n->add(chrem( [n, j], [1, 3] ), j=1..n):seq(a(n), n=0..72); # Zerinvary Lajos, Apr 07 2009

MATHEMATICA

a[n_] := Floor[(n + 1)/3] + Floor[2 (n + 1)/3]; Table[a[n], {n, 0, 90}] (* Clark Kimberling, May 28 2012 *)

a[n_] := IntegerExponent[A104537[n + 1], 2];

Table[a[n], {n, 0, 90}]  (* Gerry Martens, Jul 14 2015 *)

PROG

(PARI) main(size)=my(n, k); vector(size, n, sum(k=0, n, k%3)) \\ Anders Hellström, Jul 14 2015

(PARI) first(n)=my(s); concat(0, vector(n, k, s+=k%3)) \\ Charles R Greathouse IV, Jul 14 2015

(PARI) a(n)=n\3*3+[0, 1, 3][n%3+1] \\ Charles R Greathouse IV, Jul 14 2015

CROSSREFS

Cf. A010872, A010873, A010874, A010875, A010876, A010877, A130482, A130483, A130484.

Sequence in context: A074883 A196245 A092200 * A145805 A277192 A098238

Adjacent sequences:  A130478 A130479 A130480 * A130482 A130483 A130484

KEYWORD

nonn,easy

AUTHOR

Hieronymus Fischer, May 29 2007

STATUS

approved

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Last modified November 18 02:54 EST 2017. Contains 294840 sequences.