A113778 - OEIS

%I #22 Mar 23 2024 12:20:16

%S 4,3,2,1,8,7,6,5,12,11,10,9,16,15,14,13,20,19,18,17,24,23,22,21,28,27,

%T 26,25,32,31,30,29,36,35,34,33,40,39,38,37,44,43,42,41,48,47,46,45,52,

%U 51,50,49,56,55,54,53,60,59,58,57,64,63,62,61,68,67,66

%N Invert blocks of four in the sequence of natural numbers.

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,1,-1).

%F a(n) = k*floor((n+k-1)/k)-(n-1) mod k; k=4, n=1, 2, ...

%F a(n) = n-cos(n*pi)-2*sqrt(2)*cos((2*n+1)*pi/4). - _Jaume Oliver Lafont_, Dec 10 2008

%F G.f.: x*( 4-x-x^2-x^3+3*x^4 ) / ( (1+x)*(1+x^2)*(1-x)^2 ). - _R. J. Mathar_, Apr 02 2011

%t With[{k=4}, Table[k Floor[(n+k-1)/k]-Mod[n-1, k], {n, 1, 10k}]]

%t Reverse/@Partition[Range[100],4]//Flatten (* or *) LinearRecurrence[ {1,0,0,1,-1},{4,3,2,1,8},100] (* _Harvey P. Dale_, Mar 02 2020 *)

%Y Cf. A113655.

%K nonn,easy

%O 1,1

%A _Zak Seidov_, Jan 20 2006

%E More terms from _Harvey P. Dale_, Mar 02 2020