A271479 -id:A271479 - cp's OEIS frontend

A266569 a(1) = 1; thereafter a(2k) = 4k + a(k); a(2k+1) = k + a(4k+4).

1, 5, 30, 13, 68, 42, 64, 29, 132, 88, 119, 66, 154, 92, 132, 61, 248, 168, 217, 128, 261, 163, 221, 114, 322, 206, 273, 148, 326, 192, 268, 125, 468, 316, 401, 240, 463, 293, 387, 208, 533, 345, 448, 251, 519, 313, 425, 210, 646, 422, 543, 310, 623, 381, 511

Offset: 1

Daniel Suteu, Jan 01 2016

			For n=2, a(2) = 4 + a(1) = 5.
For n=3:
a(3) = 1 + a(8);
a(8) = 2*8 + a(8/2) = 16 + a(4);
a(4) = 2*4 + a(4/2) = 8 + a(2) = 13;
a(8) = 18+13 = 29;
a(3) = 1 + 29 = 30.

Daniel Suteu, Table of n, a(n) for n = 1..10000
Daniel Suteu, Table of n, a(n) for n = 1..100000

Records (high water marks): A270811, A270812.

Cf. A270814, A271473, A271478, A271479.

A266569 := proc(n)
    option remember;
    local k;
    if n = 1 then
        1;
    elif type(n,'even') then
        2*n+procname(n/2) ;
    else
        k := (n-1)/2 ;
        k+procname(4*k+4) ;
    end if;
end proc:
seq(A266569(n),n=1..100) ; # R. J. Mathar, May 06 2016

a[1] = 1; a[n_] := a[n] = If[EvenQ@ n, 2 n + a[n/2], (n - 1)/2 + a[2 (n + 1)]]; Array[a, 55] (* Michael De Vlieger, Jan 02 2016 *)

func a((1)) { 1 }
func a(n {.is_even}) is cached { 2*n + a(n/2) }
func a(n {.is_odd }) is cached { (n-1)/2 + a(2*(n + 1)) }
1000.times { |n| say a(n) }

A271478 If n is even, a(n)=n/2, otherwise 2*n+2.

Original entry on oeis.org

0, 4, 1, 8, 2, 12, 3, 16, 4, 20, 5, 24, 6, 28, 7, 32, 8, 36, 9, 40, 10, 44, 11, 48, 12, 52, 13, 56, 14, 60, 15, 64, 16, 68, 17, 72, 18, 76, 19, 80, 20, 84, 21, 88, 22, 92, 23, 96, 24, 100, 25, 104, 26, 108, 27, 112, 28, 116, 29, 120, 30, 124, 31, 128, 32, 132, 33, 136, 34, 140, 35

Offset: 0

N. J. A. Sloane, Apr 10 2016

Arises in studying A266569.

Colin Barker, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (0,2,0,-1).

Cf. A266569, A271479.

f:=n->if n mod 2 = 0 then n/2 else 2*n+2; fi;
[seq(f(n),n=0..100)];

Table[(5 n - (-1)^n (3 n + 4) + 4)/4, {n, 0, 70}] (* Ilya Gutkovskiy, Apr 11 2016 *)

concat(0, Vec(x*(4+x)/((1-x)^2*(1+x)^2) + O(x^50))) \\ Colin Barker, Apr 11 2016

a(n) = if (n % 2, 2*n+2, n/2); \\ Michel Marcus, Apr 11 2016

for n in range(0,10**3):
    if(not n%2):print((int)(n/2))
    else:print(2*n+2)
# Soumil Mandal, Apr 11 2016

From Colin Barker, Apr 11 2016: (Start)
a(n) = 2*a(n-2)-a(n-4) for n>3.
G.f.: x*(4+x) / ((1-x)^2*(1+x)^2). (End)
a(n) = (5*n - (-1)^n*(3*n + 4) + 4)/4. - Ilya Gutkovskiy, Apr 11 2016

cp's OEIS Frontend

A266569 a(1) = 1; thereafter a(2k) = 4k + a(k); a(2k+1) = k + a(4k+4).

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