A297556 - OEIS

A297556

a(n) = a(n-1) + 16*a(n-3) - 16*a(n-4), where a(0) = 1, a(1) = 4, a(2) = 7, a(3) = 19.

1, 6, 7, 19, 99, 115, 307, 1587, 1843, 4915, 25395, 29491, 78643, 406323, 471859, 1258291, 6501171, 7549747, 20132659, 104018739, 120795955, 322122547, 1664299827, 1932735283, 5153960755, 26628797235, 30923764531, 82463372083, 426060755763, 494780232499

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OFFSET

0,2

COMMENTS

Conjecture: a(n) = least positive whose base-4 up-variation is n; see column 1 of A297553.

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) = 7, a(3) = 19.

G.f.: (1 + 5 x + x^2 - 4 x^3)/(1 - x - 16 x^3 + 16 x^4).

MATHEMATICA