A116362 Smallest m such that A116361(m) = n.

0, 1, 3, 7, 11, 23, 39, 79, 143, 287, 543, 1087, 2111, 4223, 8319, 16639, 33023, 66047, 131583, 263167, 525311, 1050623, 2099199, 4198399, 8392703, 16785407, 33562623, 67125247, 134234111, 268468223, 536903679, 1073807359, 2147549183, 4295098367, 8590065663, 17180131327, 34360000511

Offset

0,3

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (3,0,-6,4).

Formula

a(n) = 2^(n-1) + 2^floor((n+1)/2) - 1 for n > 1.

a(n) = 2*a(n-1) + 1 - 0^(n mod 2) * 2^floor(n/2) for n>2.

From Colin Barker, Mar 29 2013 and Feb 09 2015: (Start)

a(n) = 3*a(n-1)-6*a(n-3)+4*a(n-4) for n>5.

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

a(n) = 4*A005418(n-1)-1 for n>1. - Michel Marcus, Mar 12 2026

Mathematica

LinearRecurrence[{3, 0, -6, 4}, {0, 1, 3, 7, 11, 23}, 50] (* Paolo Xausa, Mar 11 2026 *)

Prog

(PARI) concat(0, Vec(-x*(4*x^4-4*x^3-2*x^2+1)/((x-1)*(2*x-1)*(2*x^2-1)) + O(x^100))) \\ Colin Barker, Feb 09 2015

Crossrefs

Cf. A005418, A116361.

Sequence in context: A112715 A106935 A308576 * A090918 A139253 A283588

Adjacent sequences: A116359 A116360 A116361 * A116363 A116364 A116365

Keyword

nonn,easy

Author

Reinhard Zumkeller, Feb 04 2006

Status

approved