A295724 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.

0, 0, 1, 2, 5, 9, 18, 31, 57, 96, 169, 281, 482, 795, 1341, 2200, 3669, 5997, 9922, 16175, 26609, 43296, 70929, 115249, 188226, 305523, 497845, 807464, 1313501, 2129157, 3459042, 5604583, 9096393, 14733744, 23895673, 38694953, 62721698, 101547723, 164531565

Offset: 0

Author

Clark Kimberling, Nov 29 2017

Keywords

• nonn
• easy

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)

Crossrefs

Cf. A001622, A000045, A005672.

Programs

Mathematica

LinearRecurrence[{1, 3, -2, -2}, {0, 0, 1, 2}, 100]

Formula

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

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