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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

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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).

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) = 0, a(1) = 0, a(2) = 1, a(3) = 2.

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

MATHEMATICA