A130489 a(n) = Sum_{k=0..n} (k mod 11) (Partial sums of A010880).

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

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 *)
Accumulate[PadRight[{}, 80, Range[0, 10]]] (* Harvey P. Dale, Jul 21 2021 *)

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