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A078339

Let u(1)=u(2)=u(3)=1 and u(n)=(-1)^n*sign(u(n-1)-u(n-2))*u(n-3); then a(n)=sum(k=1,n,sum(i=1,k,u(i))) - 3*(n-1).

1, 0, 0, 0, 1, 3, 5, 6, 8, 10, 11, 11, 11, 10, 8, 6, 5, 3, 1, 0, 0, 0, 1, 3, 5, 6, 8, 10, 11, 11, 11, 10, 8, 6, 5, 3, 1, 0, 0, 0, 1, 3, 5, 6, 8, 10, 11, 11, 11, 10, 8, 6, 5, 3, 1, 0, 0, 0, 1, 3, 5, 6, 8, 10, 11, 11, 11, 10, 8, 6, 5, 3, 1, 0, 0, 0, 1, 3, 5, 6, 8, 10, 11, 11, 11, 10, 8, 6, 5, 3, 1

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,6

COMMENTS

Note the palindromic form of the periodic part: 0,0,1,3,5,6,8,10,11,11,11,10,8,6,5,3,1,0,0.

LINKS

Table of n, a(n) for n=1..91.

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

FORMULA

Periodic with period 18.

MATHEMATICA

LinearRecurrence[{1, 0, 0, 0, 0, 0, 0, 0, -1, 1}, {1, 0, 0, 0, 1, 3, 5, 6, 8, 10}, 91] (* Ray Chandler, Aug 27 2015 *)