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A140495
Union of A052103, A052102 and A052101, uniqued and sorted.
3
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...
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
KEYWORD
nonn,easy
AUTHOR
Paul Curtz, Jun 28 2008
EXTENSIONS
Edited and extended by R. J. Mathar, Mar 02 2010
STATUS
approved