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

 

Logo

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!)
A130485 a(n) = Sum_{k=0..n} (k mod 7) (Partial sums of A010876). 21
0, 1, 3, 6, 10, 15, 21, 21, 22, 24, 27, 31, 36, 42, 42, 43, 45, 48, 52, 57, 63, 63, 64, 66, 69, 73, 78, 84, 84, 85, 87, 90, 94, 99, 105, 105, 106, 108, 111, 115, 120, 126, 126, 127, 129, 132, 136, 141, 147, 147, 148, 150, 153, 157, 162, 168, 168, 169, 171, 174, 178, 183 (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 7, 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 (1,0,0,0,0,0,1,-1).

FORMULA

a(n) = 21*floor(n/7) + A010876(n)*(A010876(n) + 1)/2.

G.f.: (Sum_{k=1..6} k*x^k)/((1-x^7)*(1-x)).

G.f.: x*(1 - 7*x^6 + 6*x^7)/((1-x^7)*(1-x)^3).

MAPLE

a:=n->add(chrem( [n, j], [1, 7] ), j=1..n):seq(a(n), n=1..70); # Zerinvary Lajos, Apr 07 2009

MATHEMATICA

LinearRecurrence[{1, 0, 0, 0, 0, 0, 1, -1}, {0, 1, 3, 6, 10, 15, 21, 21}, 70] (* Harvey P. Dale, Jul 30 2017 *)

PROG

(PARI) concat(0, Vec((1-7*x^6+6*x^7)/(1-x^7)/(1-x)^3+O(x^70))) \\ Charles R Greathouse IV, Dec 22 2011

(Magma) I:=[0, 1, 3, 6, 10, 15, 21, 21]; [n le 8 select I[n] else Self(n-1) + Self(n-7) - Self(n-8): n in [1..71]]; // G. C. Greubel, Aug 31 2019

(Sage)

def A130485_list(prec):

    P.<x> = PowerSeriesRing(ZZ, prec)

    return P(x*(1-7*x^6+6*x^7)/((1-x^7)*(1-x)^3)).list()

A130485_list(70) # G. C. Greubel, Aug 31 2019

(GAP) a:=[0, 1, 3, 6, 10, 15, 21, 21];; for n in [9..71] do a[n]:=a[n-1]+a[n-7]-a[n-8]; od; a; # G. C. Greubel, Aug 31 2019

CROSSREFS

Cf. A010872, A010873, A010874, A010875, A010877, A130481, A130482, A130483, A130484.

Sequence in context: A034175 A306698 A139131 * A115015 A231676 A056150

Adjacent sequences:  A130482 A130483 A130484 * A130486 A130487 A130488

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.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 26 08:23 EST 2022. Contains 358354 sequences. (Running on oeis4.)