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A130488 a(n) = Sum_{k=0..n} (k mod 10) (Partial sums of A010879). 8
0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 45, 46, 48, 51, 55, 60, 66, 73, 81, 90, 90, 91, 93, 96, 100, 105, 111, 118, 126, 135, 135, 136, 138, 141, 145, 150, 156, 163, 171, 180, 180, 181, 183, 186, 190, 195, 201, 208, 216, 225, 225, 226, 228, 231, 235, 240, 246, 253 (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 10, 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 (1,0,0,0,0,0,0,0,0,1,-1).

FORMULA

a(n) = 45*floor(n/10) + A010879(n)*(A010879(n) + 1)/2.

G.f.: (Sum_{k=1..9} k*x^k)/((1-x^10)*(1-x)).

G.f.: x*(1 - 10*x^9 + 9*x^10)/((1-x^10)*(1-x)^3).

MAPLE

seq(coeff(series(x*(1-10*x^9+9*x^10)/((1-x^10)*(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, 1, -1}, {0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 45}, 60] (* G. C. Greubel, Aug 31 2019 *)

PROG

(PARI) a(n) = sum(k=0, n, k % 10); \\ Michel Marcus, Apr 28 2018

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

(Sage)

def A130488_list(prec):

    P.<x> = PowerSeriesRing(ZZ, prec)

    return P(x*(1-10*x^9+9*x^10)/((1-x^10)*(1-x)^3)).list()

A130488_list(60) # G. C. Greubel, Aug 31 2019

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

CROSSREFS

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

Sequence in context: A267238 A256379 A187845 * A061076 A054632 A109453

Adjacent sequences:  A130485 A130486 A130487 * A130489 A130490 A130491

KEYWORD

nonn

AUTHOR

Hieronymus Fischer, May 31 2007

STATUS

approved

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Last modified April 17 05:36 EDT 2021. Contains 343059 sequences. (Running on oeis4.)