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

0,3

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).

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).

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 *)

Prog

(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
(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

Crossrefs

Cf. A052101, A052102, A052103, A140414.

Sequence in context: A077121 A302488 A348448 * A174873 A213172 A008810

Adjacent sequences: A140492 A140493 A140494 * A140496 A140497 A140498

Keyword

nonn

Author

Paul Curtz, Jun 28 2008

Extensions

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

Status

approved