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A222258

Lexicographically earliest injective sequence of nonnegative integers such that the sum of 8 consecutive terms is always divisible by 8.

0, 1, 2, 3, 4, 5, 6, 11, 8, 9, 10, 19, 12, 13, 14, 27, 16, 17, 18, 35, 20, 21, 22, 43, 24, 25, 26, 51, 28, 29, 30, 59, 32, 33, 34, 67, 36, 37, 38, 75, 40, 41, 42, 83, 44, 45, 46, 91, 48, 49, 50, 99, 52, 53, 54, 107, 56, 57, 58, 115, 60, 61, 62, 123, 64, 65, 66, 131, 68, 69, 70, 139, 72, 73, 74, 147, 76, 77, 78, 155, 80, 81, 82, 163, 84, 85, 86, 171, 88, 89

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OFFSET

0,3

LINKS

Table of n, a(n) for n=0..89.

E. Angelini, k-chunks sum and division by k, post to the SeqFan list, Mar 22 2013

Index entries for linear recurrences with constant coefficients, signature (0,0,0,2,0,0,0,-1).

FORMULA

a(n) = 2 a(n-4) - a(n-8).

G.f.: x*(1 + 2*x + 3*x^2 + 4*x^3 + 3*x^4 + 2*x^5 + 5*x^6)/((1 - x)*(1 + x)*(1 + x^2))^2.

a(n)=n unless n=3 (mod 4) in which case a(n)=2n-3.

PROG