A113778 Invert blocks of four in the sequence of natural numbers.

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, 26, 25, 32, 31, 30, 29, 36, 35, 34, 33, 40, 39, 38, 37, 44, 43, 42, 41, 48, 47, 46, 45, 52, 51, 50, 49, 56, 55, 54, 53, 60, 59, 58, 57, 64, 63, 62, 61, 68, 67, 66

Offset: 1

Author

Zak Seidov, Jan 20 2006

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1).

Crossrefs

Cf. A113655.

Programs

Mathematica

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

Formula

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

a(n) = n-cos(n*pi)-2*sqrt(2)*cos((2*n+1)*pi/4). - Jaume Oliver Lafont, Dec 10 2008

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

Extensions

More terms from Harvey P. Dale, Mar 02 2020