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A138587 The union of all entries of A024495, A131708 and A024493 sorted into natural order. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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 *)

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: A302600 A053436 A057546 * A099350 A191173 A240026

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

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Last modified October 18 18:10 EDT 2018. Contains 316323 sequences. (Running on oeis4.)