A059126 -id:A059126 - cp's OEIS frontend

A059155 A hierarchical sequence (S(W'2{3}c) - see A059126).

12, 120, 1008, 8160, 65472, 524160, 4194048, 33553920, 268434432, 2147481600, 17179865088, 137438945280, 1099511611392, 8796092989440, 70368744112128, 562949953290240, 4503599627108352, 36028797018439680, 288230376150663168, 2305843009211596800, 18446744073705357312

Offset: 0

Jonas Wallgren, Feb 02 2001

Vincenzo Librandi, Table of n, a(n) for n = 0..200
J. Wallgren, Hierarchical sequences
Index entries for linear recurrences with constant coefficients, signature (10, -16).

CoefficientList[Series[12/((8 x - 1) (2 x - 1)), {x, 0, 40}], x] (* Vincenzo Librandi, May 09 2014 *)

G.f.: 12/((8*x-1)*(2*x-1)). [Maksym Voznyy (voznyy(AT)mail.ru), Jul 27 2009]

a(n) = 2^(n+2)*(4^(n+1)-1). - Peter Luschny, May 08 2014

More terms from Peter Luschny, May 08 2014

A059159 A hierarchical sequence (W'2{2}*c) - see A059126.

Original entry on oeis.org

4, 8, 4, 16, 4, 8, 4, 32, 4, 8, 4, 16, 4, 8, 4, 64, 4, 8, 4, 16, 4, 8, 4, 32, 4, 8, 4, 16, 4, 8, 4, 128, 4, 8, 4, 16, 4, 8, 4, 32, 4, 8, 4, 16, 4, 8, 4, 64, 4, 8, 4, 16, 4, 8, 4, 32, 4, 8, 4, 16, 4, 8, 4, 256, 4, 8, 4, 16, 4, 8, 4, 32, 4, 8, 4, 16, 4, 8, 4, 64, 4, 8, 4, 16, 4, 8, 4, 32, 4, 8, 4

Offset: 1

Jonas Wallgren, Feb 02 2001

J. Wallgren, Hierarchical sequences

a(n)=4<Charles R Greathouse IV, Jan 06 2018

a(n) = 4*A006519(n)

A059130 A hierarchical sequence (W2{3}* - see A059126).

Original entry on oeis.org

1, 2, 1, 3, 1, 2, 1, 2, 3, 2, 4, 2, 3, 2, 1, 2, 1, 3, 1, 2, 1, 3, 4, 3, 5, 3, 4, 3, 1, 2, 1, 3, 1, 2, 1, 2, 3, 2, 4, 2, 3, 2, 1, 2, 1, 3, 1, 2, 1, 4, 5, 4, 6, 4, 5, 4, 1, 2, 1, 3, 1, 2, 1, 2, 3, 2, 4, 2, 3, 2, 1, 2, 1, 3, 1, 2, 1, 3, 4, 3, 5, 3, 4, 3, 1, 2, 1, 3, 1, 2, 1, 2, 3, 2, 4, 2, 3, 2, 1, 2, 1, 3, 1, 2, 1

Offset: 0

Jonas Wallgren, Jan 19 2001

J. Wallgren, Hierarchical sequences

A059131 A hierarchical sequence (W3{2,2}* - see A059126).

Original entry on oeis.org

1, 2, 1, 2, 3, 2, 1, 2, 1, 2, 3, 2, 3, 4, 3, 2, 3, 2, 1, 2, 1, 2, 3, 2, 1, 2, 1, 3, 4, 3, 4, 5, 4, 3, 4, 3, 1, 2, 1, 2, 3, 2, 1, 2, 1, 2, 3, 2, 3, 4, 3, 2, 3, 2, 1, 2, 1, 2, 3, 2, 1, 2, 1, 4, 5, 4, 5, 6, 5, 4, 5, 4, 1, 2, 1, 2, 3, 2, 1, 2, 1, 2, 3, 2, 3, 4, 3, 2, 3, 2, 1, 2, 1, 2, 3, 2, 1, 2, 1, 3, 4, 3, 4, 5, 4

Offset: 0

Jonas Wallgren, Jan 19 2001

J. Wallgren, Hierarchical sequences

A059135 A hierarchical sequence (S(W2{3}c) - see A059126).

Original entry on oeis.org

11, 54, 161, 396, 887, 1890, 3917, 7992, 16163, 32526, 65273, 130788, 261839, 523962, 1048229, 2096784, 4193915, 8388198, 16776785, 33553980, 67108391, 134217234, 268434941, 536870376, 1073741267, 2147483070, 4294966697, 8589933972, 17179868543, 34359737706

Offset: 0

Jonas Wallgren, Jan 19 2001

nonn

Jonas Wallgren, Hierarchical sequences
Index entries for linear recurrences with constant coefficients, signature (4, -5, 2).

Cf. A059126, A059127.

Conjectures from Colin Barker, Oct 07 2015: (Start)
a(n) = -53 + 2^(6+n) - 21*n.
a(n) = 4*a(n-1) - 5*a(n-2) + 2*a(n-3) for n > 2.
G.f.: -(10*x+11) / ((x-1)^2*(2*x-1)).
(End)
a(n) = a(n-1) + Sum_{k=0..7*2^n-1} A059127(7*2^n-7+k) with a(-1)=0. - Sean A. Irvine, Sep 12 2022

More terms from Sean A. Irvine, Sep 12 2022

A059136 A hierarchical sequence (W3{2,2}c - see A059126).

Original entry on oeis.org

4, 10, 4, 16, 22, 16, 4, 10, 4, 28, 34, 28, 4, 10, 4, 16, 22, 16, 4, 10, 4, 40, 46, 40, 4, 10, 4, 16, 22, 16, 4, 10, 4, 28, 34, 28, 4, 10, 4, 16, 22, 16, 4, 10, 4, 52, 58, 52, 4, 10, 4, 16, 22, 16, 4, 10, 4, 28, 34, 28, 4, 10, 4, 16, 22, 16, 4, 10, 4, 40, 46, 40, 4, 10, 4, 16, 22, 16

Offset: 0

Jonas Wallgren, Jan 19 2001

Jonas Wallgren, Hierarchical sequences

Cf. A059126, A059128.

a(n) = A059128(3*n) + A059128(3*n+1) + A059128(3*n+2). - Sean A. Irvine, Sep 12 2022

A059139 A hierarchical sequence (W2{2}*c - see A059126).

Original entry on oeis.org

4, 7, 4, 10, 4, 7, 4, 13, 4, 7, 4, 10, 4, 7, 4, 16, 4, 7, 4, 10, 4, 7, 4, 13, 4, 7, 4, 10, 4, 7, 4, 19, 4, 7, 4, 10, 4, 7, 4, 13, 4, 7, 4, 10, 4, 7, 4, 16, 4, 7, 4, 10, 4, 7, 4, 13, 4, 7, 4, 10, 4, 7, 4, 22, 4, 7, 4, 10, 4, 7, 4, 13, 4, 7, 4, 10, 4, 7, 4, 16, 4, 7, 4, 10, 4, 7, 4, 13, 4, 7, 4, 10, 4

Offset: 0

Jonas Wallgren, Jan 19 2001

Let the general sequence H(a,b,n) = a*A007814(n+1) + b, then this sequence is H(3,4). Other hierarchical sequences of this type are A059132 (H(6,4)), A059141 (H(7,11)), A059144 (H(9,15)), A059134 (H(21,11)), A059137 (H(36,18)).

Ralf Stephan, Some divide-and-conquer sequences ...
J. Wallgren, Hierarchical sequences

a(n) = 4 + 3*A007814(n). a(2n) = 4, a(2n+1) = a(n) + 3. - Ralf Stephan, Oct 09 2003

A059143 A hierarchical sequence (W3{2,2}*c - see A059126).

Original entry on oeis.org

4, 7, 4, 7, 10, 7, 4, 7, 4, 10, 13, 10, 4, 7, 4, 7, 10, 7, 4, 7, 4, 13, 16, 13, 4, 7, 4, 7, 10, 7, 4, 7, 4, 10, 13, 10, 4, 7, 4, 7, 10, 7, 4, 7, 4, 16, 19, 16, 4, 7, 4, 7, 10, 7, 4, 7, 4, 10, 13, 10, 4, 7, 4, 7, 10, 7, 4, 7, 4, 13, 16, 13, 4, 7, 4, 7, 10, 7, 4, 7, 4, 10, 13, 10, 4, 7, 4, 7, 10

Offset: 0

Jonas Wallgren, Jan 19 2001

Jonas Wallgren, Hierarchical sequences

Cf. A001511, A059126, A059131, A059144, A059145.

a(n) = A059131(3*n) + A059131(3*n+1) + A059131(3*n+2). - Sean A. Irvine, Sep 13 2022

A059145 A hierarchical sequence (S(W3{2,2}*cc) - see A059126).

Original entry on oeis.org

15, 54, 141, 324, 699, 1458, 2985, 6048, 12183, 24462, 49029, 98172, 196467, 393066, 786273, 1572696, 3145551, 6291270, 12582717, 25165620, 50331435, 100663074, 201326361, 402652944, 805306119, 1610612478, 3221225205, 6442450668, 12884901603, 25769803482

Offset: 0

Jonas Wallgren, Jan 19 2001

nonn

Jonas Wallgren, Hierarchical sequences
Index entries for linear recurrences with constant coefficients, signature (4, -5, 2).

Cf. A059126.

Conjectures from Colin Barker, Oct 07 2015: (Start)
a(n) = 3*(-11 + 2^(4+n) - 3*n) = 3*A109363(n+2).
a(n) = 4*a(n-1) - 5*a(n-2) + 2*a(n-3) for n > 2.
G.f.: 3*(2*x-5) / ((x-1)^2*(2*x-1)).
(End)

More terms from Sean A. Irvine, Sep 13 2022

A059148 A hierarchical sequence (W'3{2,2} - see A059126).

Original entry on oeis.org

1, 2, 1, 4, 8, 4, 1, 2, 1, 16, 32, 16, 64, 128, 64, 16, 32, 16, 1, 2, 1, 4, 8, 4, 1, 2, 1, 256, 512, 256, 1024, 2048, 1024, 256, 512, 256, 1, 2, 1, 4, 8, 4, 1, 2, 1, 16, 32, 16, 64, 128, 64, 16, 32, 16, 1, 2, 1, 4, 8, 4, 1, 2, 1, 4096, 8192, 4096, 16384, 32768, 16384, 4096

Offset: 0

Jonas Wallgren, Feb 01 2001

J. Wallgren, Hierarchical sequences

cp's OEIS Frontend

A059155 A hierarchical sequence (S(W'2{3}c) - see A059126).

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A059159 A hierarchical sequence (W'2{2}*c) - see A059126.

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A059130 A hierarchical sequence (W2{3}* - see A059126).

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A059131 A hierarchical sequence (W3{2,2}* - see A059126).

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A059135 A hierarchical sequence (S(W2{3}c) - see A059126).

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A059136 A hierarchical sequence (W3{2,2}c - see A059126).

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A059139 A hierarchical sequence (W2{2}*c - see A059126).

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A059143 A hierarchical sequence (W3{2,2}*c - see A059126).

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A059145 A hierarchical sequence (S(W3{2,2}*cc) - see A059126).

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A059148 A hierarchical sequence (W'3{2,2} - see A059126).

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