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A049940 a(n) = a(1) + a(2) + ... + a(n-1) + a(m) for n >= 3, where m = 2*n - 3 - 2^(p+1) and p is the unique integer such that 2^p < n - 1 <= 2^(p+1) with a(1) = a(2) = 1. 8
1, 1, 3, 6, 14, 26, 54, 119, 278, 503, 1008, 2027, 4094, 8412, 17554, 38194, 89848, 162143, 324288, 648587, 1297214, 2594652, 5190034, 10383154, 20779768, 41631830, 83498100, 167969126, 339831072, 695251878, 1453222088, 3162777148, 7438945312, 13424668537, 26849337076, 53698674163 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..3320

FORMULA

a(n) = a(2*n - 3 - 2^ceiling(log_2(n-1))) + Sum_{i = 1..n-1} a(i) = a(A006257(n-2)) + Sum_{i = 1..n-1} a(i) for n >= 3 with a(1) = a(2) = 1. - Petros Hadjicostas, Sep 24 2019

EXAMPLE

From Petros Hadjicostas, Sep 24 2019: (Start)

a(3) = a(1) + a(2) + a(m=1) = 1 + 1 + 1 = 3 because m = A006257(3-2) = 2*3 - 3 - 2^ceiling(log[2](3-1)) = 1.

a(4) = a(1) + a(2) + a(3) + a(m=1) = 1 + 1 + 3 + 1 = 6 because m = A006257(4-2) = 2*4 - 3 - 2^ceiling(log[2](4-1)) = 1.

a(5) = a(1) + a(2) + a(3) + a(4) + a(m=3) = 1 + 1 + 3 + 6 + 3 = 14 because m = A006257(5-2) = 2*5 - 3 - 2^ceiling(log[2](5-1)) = 3.

a(6) = a(1) + a(2) + a(3) + a(4) + a(5) + a(m=1) = 1 + 1 + 3 + 6 + 14 + 1 = 26 because m = A006257(6-2) = 2*6 - 3 - 2^ceiling(log[2](6-1)) = 1.

(End)

MAPLE

a := proc(n) local vv, i; option remember; if n = 1 then vv := 1; end if; if n = 2 then vv := 1; end if; if 3 <= n then vv := 0; for i to n - 1 do vv := vv + a(i); end do; vv := vv + a(2*n - 3 - 2^ceil(log[2](n - 1))); end if; vv; end proc; # Petros Hadjicostas, Sep 24 2019

# second Maple program:

s:= proc(n) option remember; `if`(n<1, 0, a(n)+s(n-1)) end:

a:= proc(n) option remember; `if`(n<3, 1,

      s(n-1)+a(2*(n-2^ilog2(n-2))-3))

    end:

seq(a(n), n=1..36);  # Alois P. Heinz, Sep 24 2019

MATHEMATICA

s[n_] := s[n] = If[n < 1, 0, a[n] + s[n-1]];

a[n_] := a[n] = If[n < 3, 1, s[n-1] + a[2(n - 2^Floor@Log[2, n-2]) - 3]];

Array[a, 36] (* Jean-Fran├žois Alcover, Apr 23 2020, after Alois P. Heinz *)

CROSSREFS

Cf. A006257, A049939, A049960, A049964.

Sequence in context: A006906 A324703 A120940 * A265947 A323450 A051749

Adjacent sequences:  A049937 A049938 A049939 * A049941 A049942 A049943

KEYWORD

nonn

AUTHOR

Clark Kimberling

EXTENSIONS

Name edited by and more terms from Petros Hadjicostas, Sep 24 2019

STATUS

approved

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Last modified April 13 00:24 EDT 2021. Contains 342934 sequences. (Running on oeis4.)