|
%I #25 Sep 08 2022 08:44:48
%S 1,11,-3952,-529713,-16756480,-243891793,-2173796352,-13805455393,
%T -68289495040,-277269756129,-938082635776,-2395420006033,0,
%U 83695120256591,1227224552173568,15277275236695743,184602783918325760
%N a(n) = 12^n - n^12.
%C Conjecture: satisfies a linear recurrence having signature (25, -234, 1222, -4147, 9867, -17160, 22308, -21879, 16159, -8866, 3510, -949, 157, -12). - _Harvey P. Dale_, Jan 27 2019
%C The conjecture above is correct. From the general formula for {a(n)} we can see that the roots for the characteristic polynomial are one 12 and thirteen 1's, so the characteristic polynomial is (x - 12)*(x - 1)^13 = x^14 - 25*x^13 + 234*x^12 - ... + 12, with corresponding recurrence coefficients 25, -234, ..., -12. - _Jianing Song_, Jan 28 2019
%H Vincenzo Librandi, <a href="/A024152/b024152.txt">Table of n, a(n) for n = 0..300</a>
%H <a href="/index/Rec#order_14">Index entries for linear recurrences with constant coefficients</a>, signature (25,-234,1222,-4147,9867,-17160,22308,-21879,16159,-8866,3510,-949,157,-12).
%t Table[12^n-n^12,{n,0,30}] (* _Harvey P. Dale_, Jan 27 2019 *)
%o (Magma) [12^n-n^12: n in [0..20]]; // _Vincenzo Librandi_, Jun 30 2011
%Y Cf. A024012, A024026, A058794, A024040, A024054, A024068, A024082, A024096, A024110, A024124, A024138. - _Vladimir Joseph Stephan Orlovsky_, Jan 15 2009
%K sign,easy
%O 0,2
%A _N. J. A. Sloane_
|
