A297555 a(n) = a(n-1) + 16*a(n-3) - 16*a(n-4), where a(0) = 1, a(1) = 4, a(2) = 8, a(3) = 12, a(4) = 76.

1, 4, 8, 12, 76, 140, 204, 1228, 2252, 3276, 19660, 36044, 52428, 314572, 576716, 838860, 5033164, 9227468, 13421772, 80530636, 147639500, 214748364, 1288490188, 2362232012, 3435973836, 20615843020, 37795712204, 54975581388, 329853488332, 604731395276

Offset

0,2

Comments

Conjecture: a(n) = least positive whose base-4 down-variation is n; see column 1 of A297552.

Links

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

Index entries for linear recurrences with constant coefficients, signature (1,0,16,-16)

Formula

a(n) = a(n-1) + 16*a(n-3) - 16*a(n-4), where a(0) = 1, a(1) = 4, a(2) = 8, a(3) = 12, a(4) = 76.

G.f.: (1 + 3 x + 4 x^2 - 12 x^3 + 16 x^4)/(1 - x - 16 x^3 + 16 x^4)

Mathematica

Join[{1}, LinearRecurrence[{1, 0, 16, -16}, {4, 8, 12, 76}, 40]]

Crossrefs

Cf. A297552.

Sequence in context: A083492 A137337 A061517 * A058759 A237519 A311665

Adjacent sequences: A297552 A297553 A297554 * A297556 A297557 A297558

Keyword

nonn,easy

Author

Clark Kimberling, Jan 21 2018

Status

approved