A049964 - OEIS

A049964

a(n) = a(1) + a(2) + ... + a(n-1) + a(m) for n >= 4, 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) = 1, a(2) = 3, and a(3) = 1.

1, 3, 1, 6, 12, 24, 48, 107, 250, 453, 906, 1823, 3682, 7566, 15788, 34352, 80810, 145833, 291666, 583343, 1166722, 2333646, 4667948, 9338672, 18689450, 37443922, 75098700, 151072456, 305646138, 625313778, 1307036806, 2844621050, 6690632768, 12074228731, 24148457462, 48296914935, 96593829906

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OFFSET

1,2

LINKS

Table of n, a(n) for n=1..37.

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 >= 4 with a(1) = 1, a(2) = 3, and a(3) = 1. - Petros Hadjicostas, Sep 24 2019

EXAMPLE

From Petros Hadjicostas, Sep 24 2019: (Start)

a(4) = a(1) + a(2) + a(3) + a(m=1) = 1 + 3 + 1 + 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 + 3 + 1 + 6 + 1 = 12 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 + 3 + 1 + 6 + 12 + 1 = 24 because m = A006257(6-2) = 2*6 - 3 - 2^ceiling(log_2(6-1)) = 1.

(End)

MAPLE

a := proc(n) option remember; if n<4 then return [1, 3, 1][n] fi; add(a(i), i=1..n-1) + a(2*(n-2) - Bits:-Iff(n-2, n-2)) end: seq(a(n), n=1..37); # Petros Hadjicostas, Sep 24 2019, courtesy of Peter Luschny

CROSSREFS

Cf. A006257, A049939, A049940, A049960.

Sequence in context: A064282 A267849 A087644 * A143984 A051124 A193091

Adjacent sequences: A049961 A049962 A049963 * A049965 A049966 A049967

KEYWORD

nonn

AUTHOR

Clark Kimberling

EXTENSIONS

Name edited by and more terms from Petros Hadjicostas, Sep 23 2019

STATUS

approved