A138587 The union of all entries of A024495, A131708 and A024493 sorted into natural order.

0, 1, 2, 3, 5, 6, 10, 11, 21, 22, 42, 43, 85, 86, 170, 171, 341, 342, 682, 683, 1365, 1366, 2730, 2731, 5461, 5462, 10922, 10923, 21845, 21846, 43690, 43691, 87381, 87382, 174762, 174763, 349525, 349526, 699050, 699051, 1398101, 1398102, 2796202, 2796203, 5592405

Offset

0,3

Comments

The three sequences of the definition share the same special recurrence which reflects that each equals its own sequence of third differences.

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (-1,1,1,2,2).

Formula

a(n+8) == a(n) (mod 10), n > 1.

a(2*n+1) - a(2*n) = 1.

a(2*n) = A000975(n+1), n>0 (bisection).

From R. J. Mathar, Nov 22 2009: (Start)

a(n) = -a(n-1) +a(n-2) +a(n-3) +2*a(n-4) +2*a(n-5), n>6.

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

Mathematica

CoefficientList[Series[x*(3*x + 4*x^2 + 5*x^3 + 4*x^4 + 2*x^5 + 1)/((1 + x)*(1 - 2*x^2)*(1 + x^2)), {x, 0, 50}], x] (* G. C. Greubel, Oct 03 2017 *)
LinearRecurrence[{-1, 1, 1, 2, 2}, {0, 1, 2, 3, 5, 6, 10}, 50] (* Harvey P. Dale, Feb 18 2023 *)

Prog

(PARI) x='x+O('x^50); concat(0, Vec(x*(3*x+4*x^2+5*x^3+4*x^4 +2*x^5+ 1)/((1+x)*(1-2*x^2)*(1+x^2)))) \\ G. C. Greubel, Oct 03 2017

Crossrefs

Sequence in context: A053436 A057546 A339514 * A099350 A337218 A306296

Adjacent sequences: A138584 A138585 A138586 * A138588 A138589 A138590

Keyword

nonn

Author

Paul Curtz, May 13 2008

Extensions

Edited and extended by R. J. Mathar, Nov 22 2009

Status

approved