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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.

User: Krishnamurthy Balasubraniam

Krishnamurthy Balasubraniam's wiki page.

Krishnamurthy Balasubraniam has authored 3 sequences.

A200561 Expansion of -2*x / ( (2*x-1)*(4*x^2+3*x+1) ).

Original entry on oeis.org

2, -2, 6, 6, -10, 70, -42, 102, 374, -506, 2070, -90, 182, 16198, -16554, 50406, 46070, -77690, 573078, -359898, 884534, 2980294, -4090410, 17127270, -1465738, 2996998, 131089686, -136821594, 422976950, 352097350, -600716202, 4688726502, -3073380106, 7645103494, 23717948310, -33014782170, 141611506742
Offset: 1

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Author

Krishnamurthy Balasubraniam, Nov 19 2011

Keywords

Links

Formula

a(n) = -a(n-1) +2*a(n-2) +8*a(n-3).
7*a(n) = 2^(n+1) -2*(-1)^n*(2*A049072(n-1)+A049072(n)). - R. J. Mathar, Dec 01 2011

Extensions

Definition from R. J. Mathar, Nov 19 2011

A200563 Expansion of -2*x*(1+4*x) / ((2*x-1)*(4*x^2+3*x+1)).

Original entry on oeis.org

2, 6, -2, 30, 14, 30, 238, -66, 782, 990, 46, 8190, -178, 16926, 48238, -15810, 247694, 106590, 262318, 1932414, -555058, 6518430, 7830766, 765630, 67043342, -2865954, 143077678, 387537150, -124309426, 2044005150, 807673198, 2285861694, 15681525902, -4648416930
Offset: 1

Views

Author

Krishnamurthy Balasubraniam, Nov 19 2011

Keywords

Links

Programs

  • Magma
    I:=[2, 6, -2]; [n le 3 select I[n] else -Self(n-1)+2*Self(n-2)+8*Self(n-3): n in [1..40]]; // Vincenzo Librandi, Jul 12 2012
  • Mathematica
    LinearRecurrence[{-1,2,8}, {2,6,-2},34] (* Bruno Berselli, Dec 12 2011 *)
  • Maxima
    makelist(expand((6*4^n+(-3-sqrt(-7))^(n+1)+(-3+sqrt(-7))^(n+1))/(7*2^n)),n,1,34); /* Bruno Berselli, Dec 12 2011 */

Formula

a(n) = -a(n-1) +2*a(n-2) +8*a(n-3).
a(n) = (6*4^n+r^(n+1)+(16/r)^(n+1))/(7*2^n), where r=-3-sqrt(-7). - Bruno Berselli, Dec 12 2011

Extensions

Definition from R. J. Mathar, Nov 19 2011

A200562 Expansion of 1 / ((1 - 2*x) * (1 + 3*x + 4*x^2)) in powers of x.

Original entry on oeis.org

1, -1, 3, 3, -5, 35, -21, 51, 187, -253, 1035, -45, 91, 8099, -8277, 25203, 23035, -38845, 286539, -179949, 442267, 1490147, -2045205, 8563635, -732869, 1498499, 65544843, -68410797, 211488475, 176048675, -300358101, 2344363251, -1536690053, 3822551747, 11858974155
Offset: 0

Views

Author

Krishnamurthy Balasubraniam, Nov 19 2011

Keywords

Examples

			G.f. = 1 - x + 3*x^2 + 3*x^3 - 5*x^4 + 35*x^5 - 21*x^6 + 51*x^7 + 187*x^8 + ...

Links

Programs

  • Magma
    m:=25; R:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-2*x)*(1+3*x+4*x^2)))); // G. C. Greubel, Aug 13 2018
  • Mathematica
    LinearRecurrence[{-1,2,8},{-1,3,3},40] (* Harvey P. Dale, Aug 03 2012 *)
CoefficientList[Series[1/((1-2*x)*(1+3*x+4*x^2)), {x, 0, 50}], x] (* G. C. Greubel, Aug 13 2018 *)
  • PARI
    {a(n) = if( n<0, polcoeff( x^3 / ((2 - x) * (4 + 3*x + x^2)) + x * O(x^-n), -n), polcoeff( 1 / ((1 - 2*x) * (1 + 3*x + 4*x^2)) + x * O(x^n), n))}; /* Michael Somos, Sep 17 2014 */
  • PARI
    x='x+O('x^50); Vec(1/((1-2*x)*(1+3*x+4*x^2))) \\ G. C. Greubel, Aug 13 2018

Formula

a(n) = -a(n-1) + 2*a(n-2) + 8*a(n-3) for all n in Z.
7*a(n) = 2^(n+1) +(-1)^n*( 5*A049072(n) -4*A049072(n-1) ). - R. J. Mathar, Nov 19 2011
a() = a(-n-3) * 2^(2*n+3) for all n in Z. - Michael Somos, Sep 17 2014
0 = a(n)*(+4*a(n+1) + 2*a(n+2)) + a(n+1)*(+a(n+1) + a(n+2)) for all n in Z. - Michael Somos, Sep 17 2014

Extensions

Definition from R. J. Mathar, Nov 19 2011
Added a(0) = 1. - Michael Somos, Sep 17 2014

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