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A298158
a(n) = a(n-1) + 3*a(n-2) -2*a(n-3) - 2*a(n-4), where a(0) = -1, a(1) = -2, a(2) = 1, a(3) = 1.
1
-1, -2, 1, 1, 10, 15, 41, 64, 137, 217, 418, 667, 1213, 1944, 3413, 5485, 9410, 15151, 25585, 41248, 68881, 111153, 184130, 297331, 489653, 791080, 1297117, 2096389, 3426274, 5539047, 9030857, 14602672, 23764601, 38432809, 62459554, 101023435, 164007277
OFFSET
0,2
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) = -2, a(2) = 1, a(3) = 1.
G.f.: (-1 - x + 6 x^2 + 4 x^3)/(1 - x - 3 x^2 + 2 x^3 + 2 x^4).
MATHEMATICA
LinearRecurrence[{1, 3, -2, -2}, {-1, -2, 1, 1}, 37] (* corrected by Georg Fischer, Apr 03 2019 *)
PROG
(PARI) x='x+O('x^37); Vec((-1 - x + 6*x^2 + 4*x^3)/(1 - x - 3*x^2 + 2*x^3 + 2*x^4)) \\ Georg Fischer, Apr 03 2019
CROSSREFS
Sequence in context: A345748 A153731 A262226 * A154989 A064307 A165883
KEYWORD
easy,sign
AUTHOR
Clark Kimberling, Feb 09 2018
EXTENSIONS
a(2)=1 corrected by Georg Fischer, Apr 03 2019
STATUS
approved