A227542 a(n) is the number of all terms preceding a(n-1) that have the same even-odd parity as a(n-1).

0, 0, 1, 0, 2, 3, 1, 2, 4, 5, 3, 4, 6, 7, 5, 6, 8, 9, 7, 8, 10, 11, 9, 10, 12, 13, 11, 12, 14, 15, 13, 14, 16, 17, 15, 16, 18, 19, 17, 18, 20, 21, 19, 20, 22, 23, 21, 22, 24, 25, 23, 24, 26, 27, 25, 26, 28, 29, 27, 28, 30, 31, 29, 30, 32, 33, 31, 32, 34, 35, 33, 34, 36, 37, 35, 36, 38, 39, 37, 38, 40, 41, 39, 40, 42, 43, 41, 42, 44, 45, 43, 44, 46

Offset: 0

Author

Andres M. Torres, Jul 15 2013

Keywords

• nonn
• easy

Comments

If a(n-1) is even, a(n) is the count of all even members preceding a(n-1). If a(n-1) is odd, then a(n) is the count of all odd members preceding a(n-1).

Examples

			{0,0}        : a(1)=0, because no values exist before a(0)=0.
{0,0,1}      : a(2)=1, because 1 even value exists before a(1)=0.
{0,0,1,0}    : a(3)=0, because no odd values exist before a(2)=1.
{0,0,1,0,2}  : a(4)=2, because 2 even values exist before a(3)=0.
{0,0,1,0,2,3}: a(5)=3, because 3 even values exist before a(4)=2.
		

Links

• Andres M. Torres, Table of n, a(n) for n = 0..9999
• Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1)

Programs

Blitz3D

;; [Blitz3D] Basic code
;; --a two index array to store counts of evens and odds
Global EvenOdd[2]
;; store the sequence in an array
Global a[10001]
eo =0 ;; eo is a temporary variable
a[1] = 0  ;; seq starts with "0"
For z=1 To 10000  ;; create about 10000 values
     eo = isOdd(a[z])
     a[z+1] = EvenOdd[eo]
     EvenOdd[eo] = EvenOdd[eo] +1
Next
;; returns 1 if v is ODD, else returns zero
Function isOdd(v)
     Return v Mod 2
End Function
Function isEven(v)
     Return (v Mod 2)=0
End Function

Maple

A227542 := proc(n)
    option remember;
    local pari,a,i ;
    if n = 0 then
        0;
    else
        pari := type(procname(n-1),'even') ;
        a := 0 ;
        for i from 0 to n-2 do
            if type(procname(i),'even') = pari then
                a := a+1 ;
            end if;
        end do:
        a ;
    end if;
end proc: # R. J. Mathar, Jul 22 2013

Mathematica

Join[{0,0,1},LinearRecurrence[{1,0,0,1,-1},{0,2,3,1,2},100]] (* Harvey P. Dale, Oct 01 2013 *)

PARI

a(n) = if(n==1, 0, if(n==2, 1, (-3 - (-1)^n + (2+2*I)*(-I)^n + (2-I*2)*I^n + 2*n) / 4)) \\ Colin Barker, Oct 16 2015

PARI

concat(vector(2), Vec((2*x^7-3*x^6+x^5+2*x^4-x^3+x^2)/(x^5-x^4-x+1) + O(x^100))) \\ Colin Barker, Oct 16 2015

Formula

G.f.: x^2 + x^4*(2+x-2*x^2+x^3) / ( (1+x)*(1+x^2)*(x-1)^2 ). - R. J. Mathar, Jul 22 2013

a(n) = (-3 - (-1)^n + (2+2*i)*(-i)^n + (2-i*2)*i^n + 2*n) / 4 for n>2, where i=sqrt(-1). - Colin Barker, Oct 16 2015