A010726 -id:A010726 - cp's OEIS frontend

A171494 a(n) = 2*a(n-1) for n > 1; a(0) = 6, a(1) = 16.

6, 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

Offset: 0

Klaus Brockhaus, Dec 10 2009

nonn

16*A000079 preceded by 6.
Binomial transform of A010726.
Inverse binomial transform of A171495.

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

Equals 2*A171497.

Cf. A000079 (powers of 2), A010726 (repeat 6, 10), A171495.

Join[{6},NestList[2#&,16,30]] (* Harvey P. Dale, Jan 13 2025 *)

{m=29; v=concat([6, 16], vector(m-2)); for(n=3, m, v[n]=2*v[n-1]); v}

a(n) = 2^(n+3) for n > 0; a(0) = 6.

G.f.: 2*(3+2*x)/(1-2*x).

A171496 a(n) = 6a(n-1) - 8a(n-2) for n > 1; a(0) = 6, a(1) = 28.

Original entry on oeis.org

6, 28, 120, 496, 2016, 8128, 32640, 130816, 523776, 2096128, 8386560, 33550336, 134209536, 536854528, 2147450880, 8589869056, 34359607296, 137438691328, 549755289600, 2199022206976, 8796090925056, 35184367894528

Offset: 0

Klaus Brockhaus, Dec 10 2009

Binomial transform of A171495; second binomial transform of A171494; third binomial transform of A010726.

Vincenzo Librandi, Table of n, a(n) for n = 0..500
Index entries for linear recurrences with constant coefficients, signature (6,-8).

Equals 2*A171499.

Cf. A171476, A006516, A010036, A171494, A171495, A010726, A171472, A171473.

[8*4^n-2*2^n: n in [0..30]]; // Vincenzo Librandi, Jul 18 2011

LinearRecurrence[{6,-8},{6,28},30] (* Harvey P. Dale, Dec 21 2014 *)

{m=22; v=concat([6, 28], vector(m-2)); for(n=3, m, v[n]=6*v[n-1]-8*v[n-2]); v}

a(n) = 8*4^n - 2*2^n.
G.f.: 2*(3-4*x)/((1-2*x)*(1-4*x)).
a(n) = A171476(n+1) = A006516(n+2).
a(n+1) - a(n) = A010036(n+2).
a(n) = 4*a(n-1)+2^(n+1) (with a(0)=6). - Vincenzo Librandi, Dec 04 2010
E.g.f.: 2*exp(2*x)*(2*exp(2*x) - 1)*(2*exp(2*x) + 1). - Stefano Spezia, Dec 10 2021

A171495 a(n) = 3*a(n-1)+4 for n > 0; a(0) = 6.

Original entry on oeis.org

6, 22, 70, 214, 646, 1942, 5830, 17494, 52486, 157462, 472390, 1417174, 4251526, 12754582, 38263750, 114791254, 344373766, 1033121302, 3099363910, 9298091734, 27894275206, 83682825622, 251048476870, 753145430614, 2259436291846

Offset: 0

Klaus Brockhaus, Dec 10 2009

nonn

Binomial transform of A171494; second binomial transform of A010726.

Inverse binomial transform of A171496.

Index entries for linear recurrences with constant coefficients, signature (4, -3).

Equals 2*A171498.

Cf. A010726 (repeat 6, 10), A171494, A171496.

NestList[3#+4&,6,30] (* Harvey P. Dale, Aug 25 2019 *)

{m=25; v=concat([6], vector(m-1)); for(n=2, m, v[n]=3*v[n-1]+4); v}

a(n) = 2*(4*3^n-1).

G.f.: 2*(3-x)/((1-x)*(1-3*x)).

A176403 Decimal expansion of (15+4*sqrt(15))/5.

Original entry on oeis.org

6, 0, 9, 8, 3, 8, 6, 6, 7, 6, 9, 6, 5, 9, 3, 3, 5, 0, 8, 1, 4, 3, 4, 1, 2, 3, 1, 9, 8, 2, 5, 9, 1, 9, 6, 8, 8, 6, 6, 6, 3, 3, 7, 3, 6, 4, 2, 3, 3, 2, 7, 2, 6, 6, 1, 2, 7, 0, 0, 5, 9, 0, 1, 2, 8, 9, 0, 7, 8, 6, 4, 7, 3, 5, 4, 9, 5, 8, 3, 2, 2, 6, 8, 1, 5, 4, 2, 9, 9, 0, 1, 4, 8, 6, 9, 3, 8, 8, 1, 4, 3, 3, 3, 0, 4

Offset: 1

Klaus Brockhaus, Apr 17 2010

Continued fraction expansion of (15+4*sqrt(15))/5 is A010726.

			(15+4*sqrt(15))/5 = 6.09838667696593350814...

Daniel Starodubtsev, Table of n, a(n) for n = 1..10000

Cf. A010472 (decimal expansion of sqrt(15)), A010726 (repeat 6, 10).

A176533 Decimal expansion of (15+4*sqrt(15))/3.

Original entry on oeis.org

1, 0, 1, 6, 3, 9, 7, 7, 7, 9, 4, 9, 4, 3, 2, 2, 2, 5, 1, 3, 5, 7, 2, 3, 5, 3, 8, 6, 6, 3, 7, 6, 5, 3, 2, 8, 1, 4, 4, 4, 3, 8, 9, 5, 6, 0, 7, 0, 5, 5, 4, 5, 4, 4, 3, 5, 4, 5, 0, 0, 9, 8, 3, 5, 4, 8, 1, 7, 9, 7, 7, 4, 5, 5, 9, 1, 5, 9, 7, 2, 0, 4, 4, 6, 9, 2, 3, 8, 3, 1, 6, 9, 1, 4, 4, 8, 9, 8, 0, 2, 3, 8, 8, 8, 4

Offset: 2

Klaus Brockhaus, Apr 24 2010

Continued fraction expansion of (15+4*sqrt(15))/3 is A010726 preceded by 10.

			(15+4*sqrt(15))/3 = 10.16397779494322251357...

Cf. A010472 (decimal expansion of sqrt(15)), A010726 (repeat 6, 10).

RealDigits[(15+4*Sqrt[15])/3,10,120][[1]] (* Harvey P. Dale, Nov 10 2024 *)

cp's OEIS Frontend

A171494 a(n) = 2*a(n-1) for n > 1; a(0) = 6, a(1) = 16.

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A171496 a(n) = 6*a(n-1) - 8*a(n-2) for n > 1; a(0) = 6, a(1) = 28.

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A171495 a(n) = 3*a(n-1)+4 for n > 0; a(0) = 6.

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A176403 Decimal expansion of (15+4*sqrt(15))/5.

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A176533 Decimal expansion of (15+4*sqrt(15))/3.

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Mathematica

A171496 a(n) = 6a(n-1) - 8a(n-2) for n > 1; a(0) = 6, a(1) = 28.