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A295734
a(n) = a(n-1) + 3*a(n-2) -2*a(n-3) - 2*a(n-4), where a(0) = 0, a(1) = 0, a(2) = -1, a(3) = 2.
1
0, 0, -1, 2, -1, 7, 2, 21, 15, 60, 59, 167, 194, 457, 587, 1236, 1695, 3315, 4754, 8837, 13079, 23452, 35507, 62031, 95490, 163665, 255059, 431012, 677879, 1133467, 1794962, 2977581, 4739775, 7815660, 12489899, 20502167, 32860994, 53756377, 86355227
OFFSET
0,4
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) + 3*a(n-2) -2*a(n-3) - 2*a(n-4), where a(0) = 0, a(1) = 0, a(2) = -1, a(3) = 2.
G.f.: (x^2 (-1 + 3 x))/((-1 + x + x^2) (-1 + 2 x^2)).
MATHEMATICA
LinearRecurrence[{1, 3, -2, -2}, {0, 0, -1, 2}, 100]
CROSSREFS
Sequence in context: A097411 A134929 A160413 * A197328 A352247 A136535
KEYWORD
easy,sign
AUTHOR
Clark Kimberling, Nov 30 2017
STATUS
approved