A130487 a(n) = Sum_{k=0..n} (k mod 9) (Partial sums of A010878).

0, 1, 3, 6, 10, 15, 21, 28, 36, 36, 37, 39, 42, 46, 51, 57, 64, 72, 72, 73, 75, 78, 82, 87, 93, 100, 108, 108, 109, 111, 114, 118, 123, 129, 136, 144, 144, 145, 147, 150, 154, 159, 165, 172, 180, 180, 181, 183, 186, 190, 195, 201, 208, 216, 216, 217, 219, 222, 226

Offset

0,3

Comments

Let A be the Hessenberg n X n matrix defined by A[1,j]=j mod 9, 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 (1,0,0,0,0,0,0,0,1,-1).

Formula

a(n) = 36*floor(n/9) + A010878(n)*(A010878(n) + 1)/2.

G.f.: (Sum_{k=1..8} k*x^k)/((1-x^9)*(1-x)).

G.f.: x*(1 - 9*x^8 + 8*x^9)/((1-x^9)*(1-x)^3).

Maple

seq(coeff(series(x*(1-9*x^8+8*x^9)/((1-x^9)*(1-x)^3), x, n+1), x, n), n = 0 .. 70); # G. C. Greubel, Aug 31 2019

Mathematica

Accumulate[PadRight[{}, 120, Range[0, 8]]] (* Harvey P. Dale, Dec 19 2018 *)
Accumulate[Mod[Range[0, 100], 9]] (* Harvey P. Dale, Oct 16 2021 *)

Prog

(PARI) a(n) = sum(k=0, n, k % 9); \\ Michel Marcus, Apr 28 2018
(Magma) I:=[0, 1, 3, 6, 10, 15, 21, 28, 36, 36]; [n le 10 select I[n] else Self(n-1) + Self(n-9) - Self(n-10): n in [1..71]]; // G. C. Greubel, Aug 31 2019
(Sage)
def A130487_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P(x*(1-9*x^8+8*x^9)/((1-x^9)*(1-x)^3)).list()
A130487_list(70) # G. C. Greubel, Aug 31 2019
(GAP) a:=[0, 1, 3, 6, 10, 15, 21, 28, 36, 36];; for n in [11..71] do a[n]:=a[n-1]+a[n-9]-a[n-10]; od; a; # G. C. Greubel, Aug 31 2019

Crossrefs

Cf. A010872, A010873, A010874, A010875, A010876, A010877, A130481, A130482, A130483, A130484, A130485, A130486.

Sequence in context: A124157 A033440 A067525 * A231684 A363777 A108923

Adjacent sequences: A130484 A130485 A130486 * A130488 A130489 A130490

Keyword

nonn,easy

Author

Hieronymus Fischer, May 31 2007

Status

approved