A076313 a(n) = floor(n/10) - (n mod 10).

0, -1, -2, -3, -4, -5, -6, -7, -8, -9, 1, 0, -1, -2, -3, -4, -5, -6, -7, -8, 2, 1, 0, -1, -2, -3, -4, -5, -6, -7, 3, 2, 1, 0, -1, -2, -3, -4, -5, -6, 4, 3, 2, 1, 0, -1, -2, -3, -4, -5, 5, 4, 3, 2, 1, 0, -1, -2, -3, -4, 6, 5, 4, 3, 2, 1, 0, -1, -2, -3, 7, 6, 5, 4, 3, 2, 1, 0, -1, -2, 8, 7, 6, 5, 4

Offset: 0

Author

Reinhard Zumkeller, Oct 06 2002

Keywords

• sign
• easy

Comments

For n<100 equal to the negated alternating digital sum of n (see A055017). - Hieronymus Fischer, Jun 17 2007

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,0,0,1,-1).

Crossrefs

Cf. A076314, A010879, A076309, A076310, A076311, A076312, A055017, A076314, A007953, A003132.

Programs

Haskell

a076313 = uncurry (-) . flip divMod 10 -- Reinhard Zumkeller, Jun 01 2013

Mathematica

Table[Floor[n/10]-Mod[n,10],{n,0,100}] (* or *) LinearRecurrence[{1,0,0,0,0,0,0,0,0,1,-1},{0,-1,-2,-3,-4,-5,-6,-7,-8,-9,1},100] (* Harvey P. Dale, Nov 02 2022 *)

PARI

a(n)=n\10-n%10 \\ Charles R Greathouse IV, Jan 30 2012

Formula

From Hieronymus Fischer, Jun 17 2007: (Start)

a(n) = 11*floor(n/10)-n.

a(n) = (n-11*(n mod 10))/10.

a(n) = 11*A002266(A004526(n))-n=11*A004526(A002266(n))-n.

a(n) = (n-11*A010879(n))/10.

a(n) = (n-11*A000035(n)-22*A010874(A004526(n)))/10.

a(n) = (n-11*A010874(n)-55*A000035(A002266(n)))/10.

G.f.: x*(-8*x^10+11*x^9-1)/((1-x^10)*(1-x)^2). (End)