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A295733
a(n) = a(n-1) + 3*a(n-2) -2*a(n-3) - 2*a(n-4), where a(0) = 0, a(1) = -1, a(2) = -1, a(3) = 1.
1
0, -1, -1, 1, 0, 7, 7, 26, 33, 83, 116, 247, 363, 706, 1069, 1967, 3036, 5387, 8423, 14578, 23001, 39115, 62116, 104303, 166419, 276866, 443285, 732439, 1175724, 1932739, 3108463, 5090354, 8198817, 13387475, 21586292, 35170375, 56756667, 92320258, 149076925
OFFSET
0,6
COMMENTS
a(n)/a(n-1) -> (1 + sqrt(5))/2 = golden ratio (A001622), so that a( ) has the growth rate of the Fibonacci numbers (A000045).
FORMULA
a(n) = a(n-1) + a(n-3) + a(n-4), where a(0) = 0; a(1) = -1, a(2) = -1, a(3) = 1.
G.f.: (-x + 5 x^3)/(1 - x - 3 x^2 + 2 x^3 + 2 x^4).
MATHEMATICA
LinearRecurrence[{1, 3, -2, -2}, {0, -1, -1, 1}, 100]
CROSSREFS
KEYWORD
easy,sign
AUTHOR
Clark Kimberling, Nov 30 2017
STATUS
approved