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.

A249310 Expansion of x*(1+7*x-6*x^3)/(1-8*x^2+6*x^4).

Original entry on oeis.org

1, 7, 8, 50, 58, 358, 416, 2564, 2980, 18364, 21344, 131528, 152872, 942040, 1094912, 6747152, 7842064, 48324976, 56167040, 346116896, 402283936, 2478985312, 2881269248, 17755181120, 20636450368, 127167537088, 147803987456, 910809209984, 1058613197440
Offset: 1

Views

Author

Colin Barker, Oct 25 2014

Keywords

Comments

It seems that this is also the first row of the spectral array W(sqrt(10)-2).
It also seems that, for all k>0, the first row of W(sqrt(k^2+1)-k+1) has a generating function of the form x*(1+(2*k+1)*x-2*k*x^3)/(1-(2*k+2)*x^2+2*k*x^4).

Links

Crossrefs

Cf. A007068 (k=1), A022165 (k=2), A249311 (k=4), A249312 (k=5), A249313 (k=6).

Programs

  • Mathematica
    CoefficientList[Series[(1 + 7 x - 6 x^3)/(1 - 8 x^2 + 6 x^4), {x, 0, 40}], x] (* Vincenzo Librandi, Oct 25 2014 *)
LinearRecurrence[{0,8,0,-6},{1,7,8,50},30] (* Harvey P. Dale, Sep 22 2019 *)
  • PARI
    Vec((1+7*x-6*x^3)/(1-8*x^2+6*x^4) + O(x^100))

A249312 Expansion of x*(1+11*x-10*x^3)/(1-12*x^2+10*x^4).

Original entry on oeis.org

1, 11, 12, 122, 134, 1354, 1488, 15028, 16516, 166796, 183312, 1851272, 2034584, 20547304, 22581888, 228054928, 250636816, 2531186096, 2781822912, 28093683872, 30875506784, 311812345504, 342687852288, 3460811307328, 3803499159616, 38411612232896
Offset: 1

Views

Author

Colin Barker, Oct 25 2014

Keywords

Comments

It seems that this is also the first row of the spectral array W(sqrt(26)-4).
It also seems that, for all k>0, the first row of W(sqrt(k^2+1)-k+1) has a generating function of the form x*(1+(2*k+1)*x-2*k*x^3)/(1-(2*k+2)*x^2+2*k*x^4).

Links

Crossrefs

Cf. A007068 (k=1), A022165 (k=2), A249310 (k=3), A249311 (k=4), A249313 (k=6).

Programs

  • Mathematica
    LinearRecurrence[{0,12,0,-10},{1,11,12,122},40] (* Harvey P. Dale, Feb 02 2015 *)
  • PARI
    Vec(x*(1+11*x-10*x^3)/(1-12*x^2+10*x^4) + O(x^100))

Formula

a(1)=1, a(2)=11, a(3)=12, a(4)=122, a(n)=12*a(n-2)-10*a(n-4). - Harvey P. Dale, Feb 02 2015

A249313 Expansion of x*(1+13*x-12*x^3)/(1-14*x^2+12*x^4).

Original entry on oeis.org

1, 13, 14, 170, 184, 2224, 2408, 29096, 31504, 380656, 412160, 4980032, 5392192, 65152576, 70544768, 852375680, 922920448, 11151428608, 12074349056, 145891492352, 157965841408, 1908663749632, 2066629591040, 24970594586624, 27037224177664, 326684359217152
Offset: 1

Views

Author

Colin Barker, Oct 25 2014

Keywords

Comments

It seems that this is also the first row of the spectral array W(sqrt(37)-5).
It also seems that, for all k>0, the first row of W(sqrt(k^2+1)-k+1) has a generating function of the form x*(1+(2*k+1)*x-2*k*x^3)/(1-(2*k+2)*x^2+2*k*x^4).

Links

Crossrefs

Cf. A007068 (k=1), A022165 (k=2), A249310 (k=3), A249311 (k=4), A249312 (k=5).

Programs

  • Mathematica
    CoefficientList[Series[x (1+13x-12x^3)/(1-14x^2+12x^4),{x,0,30}],x] (* or *) LinearRecurrence[{0,14,0,-12},{1,13,14,170},30] (* Harvey P. Dale, Oct 19 2018 *)
  • PARI
    Vec(x*(1+13*x-12*x^3)/(1-14*x^2+12*x^4) + O(x^100))
Showing 1-3 of 3 results.

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