A130488 a(n) = Sum_{k=0..n} (k mod 10) (Partial sums of A010879).

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

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
(Python)
def A130488(n):
    a, b = divmod(n, 10)
    return 45*a+(b*(b+1)>>1) # Chai Wah Wu, Jul 27 2022

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