A297554 - OEIS

A297554

a(n) = a(n-2) + 4*a(n-3) - 4*a(n-5), where a(0) = 1, a(1) = 4, a(2) = 7, a(3) = 12, a(4) = 19, a(5) = 28.

1, 4, 7, 12, 19, 28, 51, 76, 115, 204, 307, 460, 819, 1228, 1843, 3276, 4915, 7372, 13107, 19660, 29491, 52428, 78643, 117964, 209715, 314572, 471859, 838860, 1258291, 1887436, 3355443, 5033164, 7549747, 13421772, 20132659, 30198988, 53687091, 80530636

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OFFSET

0,2

COMMENTS

Conjecture: a(n) = least positive whose base-4 total variation is n; see A297551.

LINKS

Clark Kimberling, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (0,1,4,0,-4)

FORMULA

G.f.: (1 + 4 x + 6 x^2 + 4 x^3 - 4 x^4 - 8 x^5)/(1 - x^2 - 4 x^3 + 4 x^5).

MATHEMATICA

Join[{1}, LinearRecurrence[{0, 1, 4, 0, -4}, {4, 7, 12, 19, 28}, 40]]