A140495 - OEIS

%I #22 Sep 30 2024 01:57:37

%S 0,1,2,3,6,9,12,15,21,27,36,45,63,81,99,144,180,225,324,405,513,729,

%T 918,1161,1647,2079,2619,3726,4698,5913,8424,10611,13365,19035,23976,

%U 30213,43011,54189,68283,97200,122472,154305,219672,276777,348705,496449,625482

%N Union of A052103, A052102 and A052101, uniqued and sorted.

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

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

%H G. C. Greubel, <a href="/A140495/b140495.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,3,0,0,-3,0,0,3).

%F 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).

%t 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 *)

%o (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

%o (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

%Y Cf. A052101, A052102, A052103, A140414.

%K nonn,easy

%O 0,3

%A _Paul Curtz_, Jun 28 2008

%E Edited and extended by _R. J. Mathar_, Mar 02 2010