A158300 -id:A158300 - cp's OEIS frontend

A158303 Triangle read by rows, A007318 * (A158300 * 0^(n-k)).

1, 1, 2, 1, 4, 2, 1, 6, 6, 8, 1, 8, 12, 32, 8, 1, 10, 20, 80, 40, 32, 1, 12, 30, 160, 120, 192, 32, 1, 14, 42, 280, 280, 672, 224, 128, 1, 16, 56, 448, 560, 1792, 896, 1024, 128, 1, 18, 72, 672, 1008, 4032, 2688, 4608, 1152, 512

Offset: 0

Gary W. Adamson, Mar 15 2009

			First few rows of the triangle =
1;
1, 2;
1, 4, 2;
1, 6, 6, 8;
1, 8, 12, 32, 8;
1, 10, 20, 80, 40, 32;
1, 12, 30, 160, 120, 192, 32;
1, 14, 42, 280, 280, 672, 224, 128;
1, 16, 56, 448, 560, 1792, 896, 1024, 128;
1, 18, 72, 672, 1008, 4032, 2688, 4608, 1152, 512;
1, 20, 90, 960, 1680, 8064, 6720, 15360, 5760, 5120, 512;
...

Cf. A158300, A122983 (row sums), A054879, A066443

Triangle read by rows, A007318 * (A158300 * 0^(n-k)). Equals binomial transform of an infinite lower triangular matrix with A158300: (1, 2, 2, 8, 8, 32, 32,...) as the main diagonal and the rest zeros.

A158302 "1" followed by repeats of 2^k deleting all 4^k, k>0.

Original entry on oeis.org

1, 2, 2, 8, 8, 32, 32, 128, 128, 512, 512, 2048, 2048, 8192, 8192, 32768, 32768, 131072, 131072, 524288, 524288, 2097152, 2097152, 8388608, 8388608, 33554432, 33554432, 134217728, 134217728, 536870912, 536870912, 2147483648, 2147483648, 8589934592

Offset: 0

Gary W. Adamson, Mar 15 2009

Binomial transform = A122983: (1, 3, 7, 21, 61, 183,...). Equals right border of triangle A158301.
Also the order of the graph automorphism group of the n+1 X n+1 black bishop graph. - Eric W. Weisstein, Jun 27 2017
For n > 1, also the order of the graph automorphism group of the n X n white bishop graph. - Eric W. Weisstein, Jun 27 2017

			Given "1" followed by repeats of powers of 2: (1, 2, 2, 4, 4, 8, 8, 16, 16,...);
delete powers of 4: (4, 16, 64, 156,...) leaving A158300:
(1, 2, 2, 8, 8, 32, 32, 128, 128,...).

Eric Weisstein's World of Mathematics, Black Bishop Graph
Eric Weisstein's World of Mathematics, Graph Automorphism
Eric Weisstein's World of Mathematics, White Bishop Graph
Index entries for linear recurrences with constant coefficients, signature (0, 4).

Cf. A122983, A158301, A154388

1,seq(4^floor((n+1)/2)/2, n=1..33); # Peter Luschny, Jul 02 2020

Join[{1}, Flatten[Table[{2^n, 2^n}, {n, 1, 41, 2}]]] (* Harvey P. Dale, Jan 24 2013 *)
Join[{1}, Table[2^(2 Ceiling[n/2] - 1), {n, 20}]] (* Eric W. Weisstein, Jun 27 2017 *)
Join[{1}, 2^(2 Ceiling[Range[20]/2] - 1)] (* Eric W. Weisstein, Jun 27 2017 *)

1 followed by repeats of powers of 2, deleting powers of 4: (4, 16, 64,...). Inverse binomial transform of A122983 starting (1, 3, 7, 21, 61, 183,...).
For n > 3: a(n) = a(n-1)*a(n-2)/a(n-3). [Reinhard Zumkeller, Mar 06 2011]
For n > 3: a(n) = 4a(n-2). [Charles R Greathouse IV, Feb 06 2011]
a(n) = Sum_{k, 0<=k<=n} A154388(n,k)*2^k. - Philippe Deléham, Dec 17 2011
G.f.: (1+2*x-2*x^2)/(1-4*x^2). - Philippe Deléham, Dec 17 2011

More terms from Harvey P. Dale, Jan 24 2013

A158301 Denominator of Bernoulli(n, -5/6).

Original entry on oeis.org

1, 3, 36, 27, 6480, 972, 326592, 34992, 8398080, 1259712, 665127936, 45349632, 990435962880, 1632586752, 78364164096, 58773123072, 239794342133760, 2115832430592, 13507474236899328, 76169967501312, 201088714203463680

Offset: 0

N. J. A. Sloane, Nov 08 2009

Vincenzo Librandi, Table of n, a(n) for n = 0..250

For numerators see A158300.

Table[Denominator[BernoulliB[n, -5/6]], {n, 0, 50}] (* Vincenzo Librandi, Mar 19 2014 *)

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A158303 Triangle read by rows, A007318 * (A158300 * 0^(n-k)).

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A158302 "1" followed by repeats of 2^k deleting all 4^k, k>0.

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A158301 Denominator of Bernoulli(n, -5/6).

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