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A130486 a(n) = Sum_{k=0..n} (k mod 8) (Partial sums of A010877). 13
0, 1, 3, 6, 10, 15, 21, 28, 28, 29, 31, 34, 38, 43, 49, 56, 56, 57, 59, 62, 66, 71, 77, 84, 84, 85, 87, 90, 94, 99, 105, 112, 112, 113, 115, 118, 122, 127, 133, 140, 140, 141, 143, 146, 150, 155, 161, 168, 168, 169, 171, 174, 178, 183, 189, 196, 196, 197, 199, 202, 206 (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 8, 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) = 28*floor(n/8) + A010877(n)*(A010877(n) + 1)/2.

G.f.: g(x) = (Sum_{k=1..7} k*x^k)/((1-x^8)(1-x)).

Also, g(x) = x(7x^8-8x^7+1)/((1-x^8)(1-x)^3).

MATHEMATICA

Array[28 Floor[#1/8] + #2 (#2 + 1)/2 & @@ {#, Mod[#, 8]} &, 61, 0] (* Michael De Vlieger, Apr 28 2018 *)

Accumulate[PadRight[{}, 100, Range[0, 7]]] (* Harvey P. Dale, Dec 21 2018 *)

PROG

(PARI) a(n) = sum(k=0, n, k % 8); \\ Michel Marcus, Apr 28 2018

CROSSREFS

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

Sequence in context: A184009 A105334 A249736 * A054636 A231680 A124158

Adjacent sequences:  A130483 A130484 A130485 * A130487 A130488 A130489

KEYWORD

nonn

AUTHOR

Hieronymus Fischer, May 31 2007

STATUS

approved

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Last modified February 17 17:12 EST 2019. Contains 320222 sequences. (Running on oeis4.)