A081597 - OEIS

%I #22 Sep 08 2022 08:45:09

%S 0,1,2,3,4,5,6,7,8,9,6,7,8,9,10,11,12,13,14,15,12,13,14,15,16,17,18,

%T 19,20,21,18,19,20,21,22,23,24,25,26,27,24,25,26,27,28,29,30,31,32,33,

%U 30,31,32,33,34,35,36,37,38,39,36,37,38,39,40,41,42,43,44,45,42,43,44,45,46,47

%N Let n = 10*x + y where 0 <= y <= 9, x >= 0. Then a(n) = 6*x + y.

%H Vincenzo Librandi, <a href="/A081597/b081597.txt">Table of n, a(n) for n = 0..2000</a>

%F G.f.: -x*(3*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 - 4*floor(n/10). [_Bruno Berselli_, Jun 24 2014]

%F a(n) = a(n-1) + a(n-10) - a(n-11) for n > 10. - _Chai Wah Wu_, Apr 25 2017

%p A081597:=n->n-4*floor(n/10): seq(A081597(n), n=0..150); # _Wesley Ivan Hurt_, Apr 25 2017

%t CoefficientList[Series[-x (3 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 *)

%o (PARI) my(n, x, y); vector(200, n, y=(n-1)%10; x=(n-1-y)\10; 6*x+y) \\ _Colin Barker_, Jun 24 2014

%o (Magma) k:=6; [n-(10-k)*Floor(n/10): n in [0..10]]; // _Bruno Berselli_, Jun 24 2014

%Y Cf. A081502. Different from A028901.

%K nonn,easy

%O 0,3

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