A140495 Union of A052103, A052102 and A052101, uniqued and sorted.

0, 1, 2, 3, 6, 9, 12, 15, 21, 27, 36, 45, 63, 81, 99, 144, 180, 225, 324, 405, 513, 729, 918, 1161, 1647, 2079, 2619, 3726, 4698, 5913, 8424, 10611, 13365, 19035, 23976, 30213, 43011, 54189, 68283, 97200, 122472, 154305, 219672, 276777, 348705, 496449, 625482

Offset: 0

Author

Paul Curtz, Jun 28 2008

Keywords

• nonn
• easy

Comments

The three sequences that are merged share the same recurrence, case p=3 in A140414.

The first differences are 1, 1, 1, 3, 3, 3, 3, 6, 6, 9, 9, 18, 18, 18, 45, 36, 45, 99, 81, 108...

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (0,0,3,0,0,-3,0,0,3).

Crossrefs

Cf. A052101, A052102, A052103, A140414.

Programs

Magma

I:=[6,9,12,15,21,27,36,45,63]; [0,1,2,3] cat [n le 9 select I[n] else 3*(Self(n-3) -Self(n-6) +Self(n-9)): n in [1..51]]; // G. C. Greubel, Apr 15 2021

Mathematica

LinearRecurrence[{0,0,3,0,0,-3,0,0,3}, {0,1,2,3,6,9,12,15,21,27,36,45,63}, 50] (* G. C. Greubel, Apr 15 2021 *)

Sage

[( x*(1+2*x+3*x^2+6*x^9+3*x^5+3*x^10+9*x^11+3*x^3+3*x^4)/(1-3*x^3+3*x^6-3*x^9) ).series(x,n+1).list()[n] for n in (0..50)] # G. C. Greubel, Apr 15 2021

Formula

G.f.: x*(1+2*x+3*x^2+6*x^9+3*x^5+3*x^10+9*x^11+3*x^3+3*x^4)/(1-3*x^3+3*x^6-3*x^9).

Extensions

Edited and extended by R. J. Mathar, Mar 02 2010