A176636 -id:A176636 - cp's OEIS frontend

A176635 a(n) = 6a(n-1)-8a(n-2) for n > 1; a(0) = 57, a(1) = 242.

57, 242, 996, 4040, 16272, 65312, 261696, 1047680, 4192512, 16773632, 67101696, 268421120, 1073713152, 4294909952, 17179754496, 68719247360, 274877448192, 1099510710272, 4398044676096, 17592182374400, 70368736837632

Offset: 0

Klaus Brockhaus, Apr 22 2010

nonn

Related to Reverse and Add trajectory of 77 in base 2: a(n) = A075253(4*n+3)/12, i.e., one twelfth of fourth quadrisection of A075253.
Second binomial transform of 57 followed by 128*A000079.
Third binomial transform of A176636.

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (6, -8).

Cf. A075253 (Reverse and Add trajectory of 77 in base 2), A176632, A176633, A176634, A176636 (repeat 57, 71), A171472.

[64*4^n-7*2^n: n in [0..25]]; // Vincenzo Librandi, Sep 24 2013

CoefficientList[Series[(57 - 100 x)/((1 - 2 x) (1 - 4 x)), {x, 0, 40}], x] (* Vincenzo Librandi, Sep 24 2013 *)
LinearRecurrence[{6,-8},{57,242},30] (* Harvey P. Dale, Jun 08 2016 *)

{m=21; v=concat([57, 242], vector(m-2)); for(n=3, m, v[n]=6*v[n-1]-8*v[n-2]); v}

a(n) = 64*4^n-7*2^n.

G.f.: (57-100*x)/((1-2*x)*(1-4*x)).

A176713 Decimal expansion of (4047+sqrt(16394397))/142.

Original entry on oeis.org

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

Offset: 2

Klaus Brockhaus, Apr 24 2010

Continued fraction expansion of (4047+sqrt(16394397))/142 is A176636.

			(4047+sqrt(16394397))/142 = 57.01408102852708894756...

Cf. A176714 (decimal expansion of sqrt(16394397)), A176636 (repeat 57, 71).

RealDigits[(4047+Sqrt[16394397])/142,10,120][[1]] (* Harvey P. Dale, Apr 09 2014 *)

cp's OEIS Frontend

A176635 a(n) = 6a(n-1)-8a(n-2) for n > 1; a(0) = 57, a(1) = 242.

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A176713 Decimal expansion of (4047+sqrt(16394397))/142.

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cp's OEIS Frontend

A176635 a(n) = 6*a(n-1)-8*a(n-2) for n > 1; a(0) = 57, a(1) = 242.

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Magma

Mathematica

PARI

Formula

A176713 Decimal expansion of (4047+sqrt(16394397))/142.

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Author

Keywords

Comments

Examples

Crossrefs

Programs

Mathematica

A176635 a(n) = 6a(n-1)-8a(n-2) for n > 1; a(0) = 57, a(1) = 242.