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A130489 a(n) = Sum_{k=0..n} (k mod 11) (Partial sums of A010880). 4
0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 55, 56, 58, 61, 65, 70, 76, 83, 91, 100, 110, 110, 111, 113, 116, 120, 125, 131, 138, 146, 155, 165, 165, 166, 168, 171, 175, 180, 186, 193, 201, 210, 220, 220, 221, 223, 226, 230, 235, 241, 248, 256, 265, 275, 275, 276 (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 11, 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 (1,0,0,0,0,0,0,0,0,0,1,-1).

FORMULA

a(n) = 55*floor(n/11) + A010880(n)*(A010880(n) + 1)/2.

G.f.: (Sum_{k=1..10} k*x^k)/((1-x^11)*(1-x)).

G.f.: x*(1 - 11*x^10 + 10*x^11)/((1-x^11)*(1-x)^3).

MAPLE

seq(coeff(series(x*(1-11*x^10+10*x^11)/((1-x^11)*(1-x)^3), x, n+1), x, n), n = 0 .. 60); # G. C. Greubel, Aug 31 2019

MATHEMATICA

LinearRecurrence[{1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1}, {0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 55}, 60] (* G. C. Greubel, Aug 31 2019 *)

PROG

(PARI) a(n) = sum(k=0, n, k % 11); \\ Michel Marcus, Apr 28 2018

(MAGMA) I:=[0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 55]; [n le 12 select I[n] else Self(n-1) + Self(n-11) - Self(n-12): n in [1..61]]; // G. C. Greubel, Aug 31 2019

(Sage)

def A130489_list(prec):

    P.<x> = PowerSeriesRing(ZZ, prec)

    return P(x*(1-11*x^10+10*x^11)/((1-x^11)*(1-x)^3)).list()

A130489_list(60) # G. C. Greubel, Aug 31 2019

(GAP) a:=[0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 55];; for n in [13..61] do a[n]:=a[n-1]+a[n-11]-a[n-12]; od; a; # G. C. Greubel, Aug 31 2019

CROSSREFS

Cf. A010872, A010873, A010874, A010875, A010876, A010877, A010878, A010879, A130481, A130482, A130483, A130484, A130485, A130486, A130487, A130488.

Sequence in context: A071817 A033442 A105335 * A211024 A261422 A262544

Adjacent sequences:  A130486 A130487 A130488 * A130490 A130491 A130492

KEYWORD

nonn

AUTHOR

Hieronymus Fischer, May 31 2007

STATUS

approved

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Last modified July 10 00:25 EDT 2020. Contains 335570 sequences. (Running on oeis4.)