A113778 - OEIS

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

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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}]]