A012814 - OEIS

%I #42 Sep 08 2022 08:44:38

%S 0,1,5,21,86,351,1432,5842,23833,97229,396655,1618192,6601569,

%T 26931732,109870576,448227521,1828587033,7459895657,30433357674,

%U 124155792775,506505428836,2066337330754,8429820731201

%N Take every 5th term of Padovan sequence A000931, beginning with the third term.

%H Vincenzo Librandi, <a href="/A012814/b012814.txt">Table of n, a(n) for n = 0..1000</a>

%H Ulrich Brenner, Anna Hermann, and Jannik Silvanus, <a href="https://arxiv.org/abs/2012.05550">Constructing Depth-Optimum Circuits for Adders and AND-OR Paths</a>, arXiv:2012.05550 [cs.DM], 2020.

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (5,-4,1).

%F a(n+3) = 5*a(n+2) - 4*a(n+1) + a(n).

%F G.f.: x/(1-5*x+4*x^2-x^3). - _Colin Barker_, Feb 03 2012

%F a(n) = A012855(n+4) - A012855(n+3).

%e G.f. = x + 5*x^2 + 21*x^3 + 86*x^4 + 351*x^5 + 1432*x^6 + 5842*x^7 + ...

%t LinearRecurrence[{5, -4, 1}, {0, 1, 5}, 25] (* _Vincenzo Librandi_, Feb 03 2012 *)

%o (Magma) I:=[0, 1, 5 ]; [n le 3 select I[n] else 5*Self(n-1)-4*Self(n-2)+Self(n-3): n in [1..40]]; // _Vincenzo Librandi_, Feb 03 2012

%Y Cf. A000931, A012855.

%K nonn,easy

%O 0,3

%A _N. J. A. Sloane_

%E Initial term 0 added by _Colin Barker_, Feb 03 2012