A297445 a(n) = a(n-1) + 9*a(n-2) - 9*a(n-3), where a(0) = 1, a(1) = 5, a(2) = 11.

1, 5, 11, 47, 101, 425, 911, 3827, 8201, 34445, 73811, 310007, 664301, 2790065, 5978711, 25110587, 53808401, 225995285, 484275611, 2033957567, 4358480501, 18305618105, 39226324511, 164750562947, 353036920601, 1482755066525, 3177332285411, 13344795598727

Offset

0,2

Comments

Conjecture: a(n) = least positive whose base-3 up-variation is n; see A297441.

Links

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

Index entries for linear recurrences with constant coefficients, signature (1,9,-9)

Formula

a(n) = a(n-1) + 9*a(n-2) - 9*a(n-3) for n>2. - Corrected by Colin Barker, Jan 21 2018

G.f.: (1 + 4 x - 3 x^2)/(1 - x - 9 x^2 + 9 x^3).

a(n) = (-1 - (-3)^n + 2*3^(1+n)) / 4. - Colin Barker, Jan 21 2018

Maple

seq(-1/4-(-3)^n/4+3*3^n/2, n=0..40); # Robert Israel, Jan 21 2018

Mathematica

LinearRecurrence[{1, 9, -9}, {1, 5, 11}, 40]]

Prog

(PARI) Vec((1 + 4*x - 3*x^2) / ((1 - x)*(1 - 3*x)*(1 + 3*x)) + O(x^40)) \\ Colin Barker, Jan 21 2018

Crossrefs

Cf. A297442.

Sequence in context: A092358 A079029 A106953 * A149503 A149504 A149505

Adjacent sequences: A297442 A297443 A297444 * A297446 A297447 A297448

Keyword

nonn,easy

Author

Clark Kimberling, Jan 21 2018

Status

approved