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

1,1

Links

Table of n, a(n) for n=1..67.

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

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

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 *)

Crossrefs

Cf. A113655.

Sequence in context: A194750 A370350 A194743 * A295673 A155172 A253902

Adjacent sequences: A113775 A113776 A113777 * A113779 A113780 A113781

Keyword

nonn,easy

Author

Zak Seidov, Jan 20 2006

Extensions

More terms from Harvey P. Dale, Mar 02 2020

Status

approved