A295727 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) = 1.

-1, 1, 1, 1, 4, 3, 11, 10, 29, 31, 76, 91, 199, 258, 521, 715, 1364, 1951, 3571, 5266, 9349, 14103, 24476, 37555, 64079, 99586, 167761, 263251, 439204, 694263, 1149851, 1827730, 3010349, 4805311, 7881196, 12620971, 20633239, 33123138, 54018521, 86879515

Offset

0,5

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).

Links

Clark Kimberling, Table of n, a(n) for n = 0..2000

Index entries for linear recurrences with constant coefficients, signature (1, 3, -2, -2)

Formula

a(n) = a(n-1) + a(n-3) + a(n-4), where a(0) = -1, a(1) = 1, a(2) = 1, a(3) = 1.

G.f.: (1 - 3 x)/(-1 + x + x^2) + x/(-1 + 2 x^2).

Mathematica

LinearRecurrence[{1, 3, -2, -2}, {-1, 1, 1, 1}, 100]

Crossrefs

Cf. A001622, A000045, A005672.

Sequence in context: A241643 A086564 A316966 * A200073 A080777 A001166

Adjacent sequences: A295724 A295725 A295726 * A295728 A295729 A295730

Keyword

easy,sign

Author

Clark Kimberling, Nov 29 2017

Status

approved