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 1-2 of 2 results.

A192070 (A192251)/2.

Original entry on oeis.org

0, 1, 4, 24, 129, 759, 4455, 26763, 161898, 988438, 6069228, 37460952, 232160184, 1443830084, 9005809184, 56316652784, 352949825249, 2216334391919, 13941409199519, 87830683173419, 554096566907069, 3499981913717189, 22132830286939649
Offset: 1

Views

Author

Clark Kimberling, Jun 27 2011

Keywords

Comments

See A192232, A192251.

Crossrefs

Cf. A192232, A192251.

Programs

A192251 1-sequence of reduction of central binomial coefficient sequence by x^2 -> x+1.

Original entry on oeis.org

0, 2, 8, 48, 258, 1518, 8910, 53526, 323796, 1976876, 12138456, 74921904, 464320368, 2887660168, 18011618368, 112633305568, 705899650498, 4432668783838, 27882818399038, 175661366346838, 1108193133814138, 6999963827434378, 44265660573879298
Offset: 1

Views

Author

Clark Kimberling, Jun 27 2011

Keywords

Comments

See A192232, A192250.

Crossrefs

Cf. A192232, A192250, A192070.

Programs

  • Magma
    [&+[Fibonacci(k)*Binomial(2*k,k): k in [0..n]]: n in [0..28]]; // Vincenzo Librandi, Feb 04 2016
  • Mathematica
    (See A192250.)
Table[Sum[Fibonacci[i] Binomial[2 i, i], {i, 0, n - 1}], {n, 23}] (* Michael De Vlieger, Feb 01 2016 *)

Formula

a(n) = 2*A192070(n).
Conjecture: (n-1)*(n-2)*a(n) -(5*n-7)*(n-2)*a(n-1) -2*(2*n-3)*(3*n-8)*a(n-2) +4*(2*n-3)*(2*n-5)*a(n-3)=0. - R. J. Mathar, May 04 2014
a(n) = Sum_{i=0..n-1} A000045(i)*binomial(2*i, i). - John M. Campbell, Feb 01 2016
Showing 1-2 of 2 results.

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