A328985 First differences of A328984.

2, 4, -2, 6, -3, 9, -7, 11, -8, 14, -12, 16, -13, 19, -17, 21, -18, 24, -22, 26, -23, 29, -27, 31, -28, 34, -32, 36, -33, 39, -37, 41, -38, 44, -42, 46, -43, 49, -47, 51, -48, 54, -52, 56, -53, 59, -57, 61, -58, 64, -62, 66, -63, 69, -67, 71, -68, 74

Offset: 1

Author

N. J. A. Sloane, Nov 06 2019

Keywords

• sign
• easy

Comments

This is a simplified version of A328196.

Links

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

Crossrefs

Cf. A328190, A328196, A328984.

Programs

Mathematica

Differences[Table[Which[EvenQ[n],Floor[(5 n/2+1)/2],Mod[n,4]==1,10 (n-1)/4+1,True,10 (n-3)/4+7],{n,70}]] (* Harvey P. Dale, Apr 06 2021 *)

Formula

If n is a multiple of 4 then a(n) = 5*t+1 where t = n/4;

if n is 2 mod 4 then a(n) = 5*t+4 where t = (n-2)/4;

if n is 1 mod 4 then a(n) = -(5*t-2) where t = (n-1)/4;

if n i s 3 mod 4 then a(n) = -(5*t+2) where t = (n-3)/4.

From Colin Barker, Nov 07 2019: (Start)

G.f.: x*(2 + 6*x + 2*x^2 + 4*x^3 + x^4) / ((1+x)*(1-x^4)).

a(n) = -a(n-1) + a(n-4) + a(n-5) for n>5.

(End)