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A295681
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a(n) = a(n-1) + a(n-3) + a(n-4), where a(0) = 0, a(1) = 1, a(2) = 0, a(3) = 2.
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2
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0, 1, 0, 2, 3, 4, 6, 11, 18, 28, 45, 74, 120, 193, 312, 506, 819, 1324, 2142, 3467, 5610, 9076, 14685, 23762, 38448, 62209, 100656, 162866, 263523, 426388, 689910, 1116299, 1806210, 2922508, 4728717, 7651226, 12379944, 20031169, 32411112, 52442282, 84853395
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OFFSET
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0,4
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COMMENTS
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Lim_{n->inf} a(n)/a(n-1) = (1 + sqrt(5))/2 = golden ratio (A001622), so that a( ) has the growth rate of the Fibonacci numbers (A000045).
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LINKS
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FORMULA
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a(n) = a(n-1) + a(n-3) + a(n-4), where a(0) = 0, a(1) = 1, a(2) = 0, a(3) = 2.
G.f.: (-x + x^2 - 2 x^3)/(-1 + x + x^3 + x^4).
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MATHEMATICA
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LinearRecurrence[{1, 0, 1, 1}, {0, 1, 0, 2}, 100]
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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