login
A295737
a(n) = a(n-1) + 3*a(n-2) -2*a(n-3) - 2*a(n-4), where a(0) = 1, a(1) = -1, a(2) = -1, a(3) = 2.
1
1, -1, -1, 2, -1, 9, 4, 29, 25, 86, 95, 245, 308, 681, 925, 1862, 2659, 5033, 7436, 13493, 20417, 35958, 55351, 95405, 148708, 252305, 396917, 665606, 1054331, 1752705, 2790652, 4608893, 7366777, 12106742, 19407983, 31776869, 51053780, 83354937, 134146573
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) + a(n-3) + a(n-4), where a(0) = 1; a(1) = -1, a(2) = -1, a(3) = 2.
G.f.: (1 - 2 x - 3 x^2 + 8 x^3)/(1 - x - 3 x^2 + 2 x^3 + 2 x^4).
MATHEMATICA
LinearRecurrence[{1, 3, -2, -2}, {1, -1, -1, 2}, 100]
CROSSREFS
KEYWORD
easy,sign
AUTHOR
Clark Kimberling, Nov 30 2017
STATUS
approved