A306399 a(1)=1; a(n) = number of occurrences of a(n-1) if a(n-1) is odd; a(n) = number of occurrences of a(n-2) if a(n-1) is even.

1, 1, 2, 2, 2, 3, 1, 3, 2, 2, 5, 1, 4, 4, 2, 2, 7, 1, 5, 2, 2, 9, 1, 6, 6, 2, 2, 11, 1, 7, 2, 2, 13, 1, 8, 8, 2, 2, 15, 1, 9, 2, 2, 17, 1, 10, 10, 2, 2, 19, 1, 11, 2, 2, 21, 1, 12, 12, 2, 2, 23, 1, 13, 2, 2, 25, 1, 14, 14, 2, 2, 27, 1, 15, 2, 2

Offset

1,3

Links

Colin Barker, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,0,0,-1).

Formula

From Colin Barker, Aug 24 2019: (Start)

G.f.: x*(1 + x + 2*x^2 + 2*x^3 + 2*x^4 + 3*x^5 + x^6 + 3*x^7 + 2*x^8 + 2*x^9 + 5*x^10 - x^11 + 2*x^12 - 2*x^14 - 2*x^15 + x^16 - x^17 - x^18 - 2*x^19 - 2*x^20 - x^21 - x^23) / ((1 - x)^2*(1 + x + x^2 + x^3 + x^4 + x^5 + x^6 + x^7 + x^8 + x^9 + x^10)^2).

a(n) = 2*a(n-11) - a(n-22) for n>24.

(End)

Example

Since a(6) is odd, a(7) = number of occurrences of a(6). Number of occurrences of a(6)=3 up to that point is 1.
a(14) is even, so a(15) = number of occurrences of a(13). Number of occurrences of a(13)=4 up to that point is 2.

Mathematica

CoefficientList[Series[(1 + x + 2*x^2 + 2*x^3 + 2*x^4 + 3*x^5 + x^6 + 3*x^7 + 2*x^8 + 2*x^9 + 5*x^10 - x^11 + 2*x^12 - 2*x^14 - 2*x^15 + x^16 - x^17 - x^18 - 2*x^19 - 2*x^20 - x^21 - x^23)/((1 - x)^2*(1 + x + x^2 + x^3 + x^4 + x^5 + x^6 + x^7 + x^8 + x^9 + x^10)^2), {x, 0, 100}], x] (* Wesley Ivan Hurt, Aug 24 2019 *)

Prog

(VBA/Excel)
Sub 306399()
   Cells(1, 1)=1
   For n = 2 To 200
      k = 2 - (Cells(n - 1, 1) Mod 2)
      m = Cells(n - k, 1)
      S = 0
      For j = 1 To n - 1
         If Cells(j, 1) = m Then
            S = S + 1
         End If
      Next j
      Cells(n, 1) = S
   Next n
End Sub
(Python)
n, aa = 1, [1]
print(n, 1)
while n <= 75:
    sa = aa[len(aa)-2+aa[len(aa)-1]%2]
    i, a = 0, 0
    while i < len(aa):
        if sa == aa[i]:
            a = a+1
        i = i+1
    print(n, a)
    n, aa = n+1, aa+[a] # A.H.M. Smeets, Aug 23 2019
(PARI) nbo(v, i) = #select(x->(x == v[i]), v);
lista(nn) = {v = vector(nn); v[1] = 1; for (k=2, nn, if (v[k-1] % 2, v[k] = nbo(v, k-1), v[k] = nbo(v, k-2)); ); v; } \\ Michel Marcus, Aug 24 2019
(PARI) Vec(x*(1 + x + 2*x^2 + 2*x^3 + 2*x^4 + 3*x^5 + x^6 + 3*x^7 + 2*x^8 + 2*x^9 + 5*x^10 - x^11 + 2*x^12 - 2*x^14 - 2*x^15 + x^16 - x^17 - x^18 - 2*x^19 - 2*x^20 - x^21 - x^23) / ((1 - x)^2*(1 + x + x^2 + x^3 + x^4 + x^5 + x^6 + x^7 + x^8 + x^9 + x^10)^2) + O(x^80)) \\ Colin Barker, Aug 25 2019
(PARI) A306399_upto(N, c=Map([0; 1]~), L, P)=vector(N, i, [P, L]=[L, mapget(c, if(bitand(L, 1), L, P))]; mapput(~c, L, iferr(mapget(c, L)+1, E, 1)); L) \\ M. F. Hasler, Sep 02 2019

Crossrefs

Sequence in context: A103960 A242626 A360387 * A240689 A233567 A141059

Adjacent sequences: A306396 A306397 A306398 * A306400 A306401 A306402

Keyword

nonn,easy

Author

Ali Sada, Aug 22 2019

Status

approved