

A240828


a(1)=a(2)=0, a(3)=2; thereafter a(n) = Sum( a(nisa(ni1)), i=0..k1 ), where s=0, k=3.


7



0, 0, 2, 2, 4, 2, 6, 4, 8, 4, 10, 6, 12, 6, 14, 8, 16, 8, 18, 10, 20, 10, 22, 12, 24, 12, 26, 14, 28, 14, 30, 16, 32, 16, 34, 18, 36, 18, 38, 20, 40, 20, 42, 22, 44, 22, 46, 24, 48, 24, 50, 26, 52, 26, 54, 28, 56, 28, 58, 30, 60, 30, 62, 32, 64, 32, 66, 34, 68, 34, 70, 36, 72, 36, 74, 38, 76, 38, 78, 40, 80, 40
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OFFSET

1,3


COMMENTS

Is this A185048 with the leading two 1's replaced by 0's?  R. J. Mathar, Apr 17 2014.
This is true, see formulas below.  Bruno Berselli, Apr 18 2014


LINKS

N. J. A. Sloane, Table of n, a(n) for n = 1..20000
Joseph Callaghan, John J. Chew III, and Stephen M. Tanny, On the behavior of a family of metaFibonacci sequences, SIAM Journal on Discrete Mathematics 18.4 (2005): 794824. See Fig. 1.4.
Craig Knecht, Row sums of superimposed binary filled triangle.
Index entries for Hofstadtertype sequences
Index entries for linear recurrences with constant coefficients, signature (0,1,0,1,0,1).


FORMULA

From Bruno Berselli, Apr 18 2014: (Start)
G.f.: 2*x^3*(1 + x + x^2)/((1  x)^2*(1 + x)^2*(1 + x^2)).
a(n) = n  1  ((1)^n + 1)*(n  (1)^floor(n/2)  1)/4. Therefore:
a(2h+1) = 2h, a(2h) = 2*floor(h/2), or also: a(4h) = a(4h+2) = 2h, a(4h+1) = 4h, a(4h+3) = 4h+2.
a(n) = a(n2) + a(n4)  a(n6) for n>6. (End)


MAPLE

#T_s, k(n) from Callaghan et al. Eq. (1.6).
s:=0; k:=3;
a:=proc(n) option remember; global s, k;
if n <= 2 then 0
elif n = 3 then 2
else
add(a(nisa(ni1)), i=0..k1);
fi; end;
t1:=[seq(a(n), n=1..100)];


MATHEMATICA

LinearRecurrence[{0, 1, 0, 1, 0, 1}, {0, 0, 2, 2, 4, 2}, 100] (* Vincenzo Librandi, Jul 12 2015 *)


PROG

(MAGMA) [n le 3 select 2*Floor((n1)/2) else Self(nSelf(n1))+Self(n1Self(n2))+Self(n2Self(n3)): n in [1..100]]; // Bruno Berselli, Apr 18 2014
(MAGMA) [n1((1)^n+1)*(n(1)^Floor(n/2)1)/4: n in [1..80]]; // Vincenzo Librandi, Jul 12 2015


CROSSREFS

Cf. A185048.
Sequence in context: A277705 A028913 A185048 * A239240 A054929 A236628
Adjacent sequences: A240825 A240826 A240827 * A240829 A240830 A240831


KEYWORD

nonn,look,hear,easy


AUTHOR

N. J. A. Sloane, Apr 16 2014


STATUS

approved



