cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A070875 Binary expansion is 1x100...0 where x = 0 or 1.

Original entry on oeis.org

5, 7, 10, 14, 20, 28, 40, 56, 80, 112, 160, 224, 320, 448, 640, 896, 1280, 1792, 2560, 3584, 5120, 7168, 10240, 14336, 20480, 28672, 40960, 57344, 81920, 114688, 163840, 229376, 327680, 458752, 655360, 917504, 1310720, 1835008, 2621440
Offset: 0

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Author

N. J. A. Sloane, May 19 2002

Keywords

Comments

A 2-automatic sequence. - Charles R Greathouse IV, Sep 24 2012
Third row in array A228405. - Richard R. Forberg, Sep 06 2013
Conjecture: a(n) = -1 + positions of the ones in A309019(n+2) - A002487(n+2). - George Beck, Mar 26 2022
Consecutive integers for which the number of its proper nondivisors of the form 2^k (k > 0) is 2; proper nondivisors are defined in A173540 (5 has two such nondivisors: 2 and 4, 7 has 2 and 4, 10 has 4 and 8, 14 has 4 and 8, 20 has 8 and 16,...). - Lechoslaw Ratajczak, Dec 17 2024

Links

Crossrefs

Cf. A070876, A123760, A063920.

Programs

  • Magma
    [n le 2 select 2*n+3 else 2*Self(n-2): n in [1..39]]; // Bruno Berselli, Mar 01 2011
  • Mathematica
    Flatten@ NestList[ 2# &, {5, 7}, 19] (* Or *)
CoefficientList[ Series[(5 + 7 x)/(1 - 2 x^2), {x, 0, 38}], x] (* Robert G. Wilson v, May 20 2002 *)
  • PARI
    a(n)=if(n%2,7,5)<<(n\2) \\ Charles R Greathouse IV, Sep 24 2012

Formula

A093873(a(n)) = 2. - Reinhard Zumkeller, Oct 13 2006
For n>1, a(n+1) = a(n) + A000010(a(n)). - Stefan Steinerberger, Dec 20 2007
From Bruno Berselli, Mar 01 2011: (Start)
G.f.: (5+7*x)/(1-2*x^2).
a(n) = (6-(-1)^n)*2^((2*n+(-1)^n-1)/4). Therefore: a(n) = 5*2^(n/2) for n even, otherwise a(n) = 7*2^((n-1)/2).
a(n) = 2*a(n-2) for n>1. (End)
a(n+1) = A063757(n) + 6. - Philippe Deléham, Apr 13 2013
a(n) = sqrt(2*a(n-1) - (-2)^(n-1)). - Richard R. Forberg, Sep 06 2013
a(n+3) = a(n+2)*a(n+1)/a(n). - Richard R. Forberg, Sep 06 2013
For n>1, a(n) = 2*phi(a(n)) + phi(phi(a(n))). - Ivan Neretin, Feb 28 2016
a(2n) = A020714(n), a(2n+1) = A005009(n); for n>0. - Yosu Yurramendi, Jun 01 2016
From Ilya Gutkovskiy, Jun 02 2016: (Start)
E.g.f.: 7*sinh(sqrt(2)*x)/sqrt(2) + 5*cosh(sqrt(2)*x).
a(n) = 2^((n-3)/2)*(5*sqrt(2)*(1 + (-1)^n) + 7*(1 - (-1)^n)). (End)
Sum_{n>=0} 1/a(n) = 24/35. - Amiram Eldar, Mar 28 2022

Extensions

Extended by Robert G. Wilson v, May 20 2002

A048489 a(n) = 7 * 2^n - 6.

Original entry on oeis.org

1, 8, 22, 50, 106, 218, 442, 890, 1786, 3578, 7162, 14330, 28666, 57338, 114682, 229370, 458746, 917498, 1835002, 3670010, 7340026, 14680058, 29360122, 58720250, 117440506, 234881018, 469762042, 939524090, 1879048186
Offset: 0

Views

Author

Clark Kimberling

Keywords

Comments

Number of 3 X n 0-1 matrices avoiding simultaneously the right angled numbered polyomino patterns (ranpp) (00;1), (10;0) and (11;0). An occurrence of a ranpp (xy;z) in a matrix A=(a(i,j)) is a triple (a(i1,j1), a(i1,j2), a(i2,j1)) where i1Sergey Kitev, Nov 13 2004
Row sums of triangle A131115. - N. J. A. Sloane, Nov 10 2007
Equals binomial transform of [1, 7, 7, 7, ...]. - Gary W. Adamson, Apr 28 2008
Number of variations of a Componium barrel which produces n phrases. This sequence describes the variations produced by the Componium, a historical mechanical organ. Another way of describing it is: Number of base 8 n-digit numbers produced by repeating or advancing along this 14-step cycle: (0,1,2,3,4,5,6,7,6,5,4,3,2,1). Subset of A126362. - Jim Bumgardner, Dec 10 2013
a(n) = the sum of the terms in row(n) in a triangle with first column T(n,0)=
1+2*n and diagonal T(n,n)=1+4*n with T(i,j)=T(i-1,j-1) + T(i-1,j). - J. M. Bergot, May 11 2018

Links

Crossrefs

a(n)=T(6, n), array T given by A048483.
n-th difference of a(n), a(n-1), ..., a(0) is (7, 7, 7, ...).
Cf. A131115.

Programs

  • Maple
    A048489:=n->7*2^n-6: seq(A048489(n), n=0..40); # Wesley Ivan Hurt, Apr 18 2017
  • Mathematica
    CoefficientList[Series[(1 + 5 x)/((2 x - 1) (x - 1)), {x, 0, 28}], x] (* Michael De Vlieger, May 22 2018 *)
7*2^Range[0,30]-6 (* or *) LinearRecurrence[{3,-2},{1,8},30] (* Harvey P. Dale, May 19 2019 *)
  • PARI
    a(n)=7<Charles R Greathouse IV, Dec 10 2013

Formula

a(n) = A000079(n)*7-6 = A005009(n)-6. - Omar E. Pol, Dec 21 2008
a(n) = 2*a(n-1)+6 with n>0, a(0)=1. - Vincenzo Librandi, Aug 06 2010
G.f.: ( 1+5*x ) / ( (2*x-1)*(x-1) ). - R. J. Mathar, Oct 21 2012
a(n) = A063757(2*n). - Philippe Deléham, Apr 13 2013

A220753 Expansion of (1+4*x+5*x^2-x^3)/((1-x)*(1+x)*(1-2*x^2)).

Original entry on oeis.org

1, 4, 8, 11, 22, 25, 50, 53, 106, 109, 218, 221, 442, 445, 890, 893, 1786, 1789, 3578, 3581, 7162, 7165, 14330, 14333, 28666, 28669, 57338, 57341, 114682, 114685, 229370, 229373, 458746, 458749, 917498, 917501, 1835002, 1835005, 3670010, 3670013
Offset: 0

Views

Author

Philippe Deléham, Apr 13 2013

Keywords

Links

Crossrefs

Cf. A005009, A048489, A063757.

Programs

  • Magma
    m:=41; R:=PowerSeriesRing(Integers(), m); Coefficients(R!((1+4*x+5*x^2-x^3)/((1-x)*(1+x)*(1-2*x^2)))); // Bruno Berselli, Apr 13 2013
  • Mathematica
    Table[7 2^Floor[n/2] - (3/2) (3 + (-1)^n), {n, 0, 40}] (* Bruno Berselli, Apr 13 2013 *)
LinearRecurrence[{0, 3, 0, -2}, {1, 4, 8, 11}, 40] (* T. D. Noe, Apr 17 2013 *)

Formula

G.f.: (1+4*x+5*x^2-x^3)/((1-x)*(1+x)*(1-2*x^2)).
a(2n) = 7*2^n - 6 = A048489(n) = A063757(2n) = A005009(n)-6.
a(2n+1) = 7*2^n - 3 = A048489(n) + 3 = A063757(2n+1) - 3*A000225(n) = A005009(n)-3.
a(n) = a(n-1)*2 if n even.
a(n) = a(n-1)+3 if n odd.
a(n) = 3*a(n-2) - 2*a(n-4) with a(0)=1, a(1)=4, a(2)=8, a(3)=11.
a(n) = 7*2^floor(n/2) - (3/2)*(3+(-1)^n).
a(n) = A047290(A083416(n+1)). [Bruno Berselli, Apr 13 2013]
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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