OFFSET
0,2
LINKS
Ilya Gutkovskiy, Illustration
Index entries for linear recurrences with constant coefficients, signature (1,0,2,-2,0,-1,1)
FORMULA
G.f.: (1 + x + x^2 - x^3 - x^4 + x^6)/((1 - x)^3*(1 + x + x^2)^2).
a(n) = a(n-1) + 2*a(n-3) - 2*a(n-4) - a(n-6) + a(n-7).
a(n) = 1 + 10*n/9 - n^2/9 + (n/3 - 8/9)*floor(n/3) + (n/3 - 4/9)*floor((n+1)/3). - Vaclav Kotesovec, Jun 29 2016
EXAMPLE
Illustration of initial terms:
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o o o o o o
o o o o o o o o o o o o o o o o
o o o o o o o o o o o o o o o o o o o o o o o
o o o o o o o o o o o o o o o o o o o o o o o o o
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0 1 2 3 4 5 6 7 8 9
MATHEMATICA
LinearRecurrence[{1, 0, 2, -2, 0, -1, 1}, {1, 2, 3, 4, 5, 7, 9}, 65]
Table[1 + 10*n/9 - n^2/9 + (n/3 - 8/9)*Floor[n/3] + (n/3 - 4/9)*Floor[(n+1)/3], {n, 0, 100}] (* Vaclav Kotesovec, Jun 29 2016 *)
PROG
(PARI) Vec((1+x+x^2-x^3-x^4+x^6)/((1-x)^3*(1+x+x^2)^2) + O(x^99)) \\ Altug Alkan, Jul 05 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Ilya Gutkovskiy, Jun 29 2016
STATUS
approved