A081595 - OEIS

%I #16 Sep 17 2023 11:32:15

%S 0,1,2,3,4,5,6,7,8,9,4,5,6,7,8,9,10,11,12,13,8,9,10,11,12,13,14,15,16,

%T 17,12,13,14,15,16,17,18,19,20,21,16,17,18,19,20,21,22,23,24,25,20,21,

%U 22,23,24,25,26,27,28,29,24,25,26,27,28,29,30,31,32,33,28,29,30,31,32,33,34,35

%N Let n = 10x + y where 0 <= y <= 9, x >= 0. Then a(n) = 4x+y.

%H Vincenzo Librandi, <a href="/A081595/b081595.txt">Table of n, a(n) for n = 0..2000</a>

%H <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,0,0,0,0,1,-1).

%F G.f.: -x*(5*x^9 -x^8 -x^7 -x^6 -x^5 -x^4 -x^3 -x^2 -x -1) / ((x -1)^2*(x +1)*(x^4 -x^3 +x^2 -x +1)*(x^4 +x^3 +x^2 +x +1)). - _Colin Barker_, Jun 24 2014

%F a(n) = n - 6*floor(n/10). [_Bruno Berselli_, Jun 24 2014]

%t CoefficientList[Series[-x (5 x^9 - x^8 - x^7 - x^6 - x^5 - x^4 - x^3 - x^2 - x - 1)/((x - 1)^2 (x + 1) (x^4 - x^3 + x^2 - x + 1) (x^4 + x^3 + x^2 + x + 1)), {x, 0, 150}], x] (* _Vincenzo Librandi_, Jun 25 2014 *)

%t LinearRecurrence[{1,0,0,0,0,0,0,0,0,1,-1},{0,1,2,3,4,5,6,7,8,9,4},80] (* _Harvey P. Dale_, Sep 17 2023 *)

%o (PARI) my(n, x, y); vector(200, n, y=(n-1)%10; x=(n-1-y)\10; 4*x+y) \\ _Colin Barker_, Jun 24 2014

%o (Magma) k:=4; [n-(10-k)*Floor(n/10): n in [0..100]]; // _Bruno Berselli_, Jun 24 2014

%Y Cf. A081502. Different from A028899.

%K nonn

%O 0,3

%A _N. J. A. Sloane_, Apr 22 2003