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A130487 a(n) = Sum_{k=0..n} (k mod 9) (Partial sums of A010878). 11
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 (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 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

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(8x^9-9x^8+1)/((1-x^9)(1-x)^3).

PROG

(PARI) a(n) = sum(k=0, n, k % 9); \\ Michel Marcus, Apr 28 2018

CROSSREFS

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

Sequence in context: A124157 A033440 A067525 * A231684 A108923 A033441

Adjacent sequences:  A130484 A130485 A130486 * A130488 A130489 A130490

KEYWORD

nonn

AUTHOR

Hieronymus Fischer, May 31 2007

STATUS

approved

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Last modified May 21 13:21 EDT 2018. Contains 304397 sequences. (Running on oeis4.)