A137173 -id:A137173 - cp's OEIS frontend

A155559 a(n) = 2*A131577(n).

0, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 8388608, 16777216, 33554432, 67108864, 134217728, 268435456, 536870912, 1073741824, 2147483648, 4294967296, 8589934592

Offset: 0

Paul Curtz, Jan 24 2009

Essentially the same as A131577, A046055, A011782, A000079 and A034008.

Index entries for linear recurrences with constant coefficients, signature (2).

Cf. A000079, A007582, A011782, A034008, A046055, A063376, A084633, A090129, A131577, A137173.

CoefficientList[ Series[ 2x/(1 - 2x), {x, 0, 32}], x] (* Robert G. Wilson v, Aug 08 2018 *)

a(n)=if(n,2^n,0) \\ Charles R Greathouse IV, Aug 01 2016

def A155559(n): return 1<Chai Wah Wu, Sep 05 2024

a(n) = A000079(n), n>0.
a(n) = (-1)^(n+1)*A084633(n+1).
a(n) + A155543(n) = 2^n+4^n = A063376(n) = 2*A007582(n) =2*A137173(2n+1).
Conjecture: a(n) = A090129(n+3)-A090129(n+2).
G.f.: 2*x/(1-2*x). - R. J. Mathar, Jul 23 2009
E.g.f.: exp(2*x) - 1. - Stefano Spezia, Aug 26 2025

Edited by R. J. Mathar, Jul 23 2009

Extended by Omar E. Pol, Nov 19 2012

A137171 Interleaved reading of A000749 and its first to third differences.

Original entry on oeis.org

0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 2, 1, 1, 3, 3, 1, 4, 6, 4, 2, 10, 10, 6, 6, 20, 16, 12, 16, 36, 28, 28, 36, 64, 56, 64, 72, 120, 120, 136, 136, 240, 256, 272, 256, 496, 528, 528, 496, 1024, 1056, 1024, 992, 2080, 2080, 2016, 2016, 4160, 4096, 4032, 4096, 8256, 8128, 8128

Offset: 0

Paul Curtz, May 11 2008

A000749 is identical to its fourth differences, which implies that the 2nd differences equal the 5th, the 3rd differences the 6th and so on and implies that each of the sequences of these differences obeys the recurrence a(n)=4a(n-1)-6a(n-2)+4a(n-3), n > 3.
The table containing A000749 and its first differences (essentially A038505), 2nd differences (A038504) and 3rd differences (A038503) as the 4 rows is
O, 0, 0, 1, 4, 10, 20, 36, 64, ...
0, 0, 1, 3, 6, 10, 16, 28, 56, ...
0, 1, 2, 3, 4, 6, 12, 28, 64, ...
1, 1, 1, 1, 2, 6, 16, 36, 72, ...
Columns sums are 1, 2, 4, 8, 16, 32 ... = 2^n =A000079. The sequence reads this table column by column.

Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 4, 0, 0, 0, -6, 0, 0, 0, 4).

Cf. A137172, A137173.

Join[{0, 0, 0, 1},LinearRecurrence[{0, 0, 0, 4, 0, 0, 0, -6, 0, 0, 0, 4},{0, 0, 1, 1, 0, 1, 2, 1, 1, 3, 3, 1},59]] (* Ray Chandler, Sep 23 2015 *)

Edited by R. J. Mathar, Jun 28 2008

cp's OEIS Frontend

A155559 a(n) = 2*A131577(n).

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