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.

A146541 Binomial transform of A010688.

Original entry on oeis.org

1, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 8388608, 16777216, 33554432, 67108864, 134217728, 268435456, 536870912, 1073741824, 2147483648, 4294967296, 8589934592
Offset: 0

Views

Author

Philippe Deléham, Oct 31 2008

Keywords

Comments

Hankel transform is := 1,-48,0,0,0,0,0,0,0,...

Links

Crossrefs

Cf. A000007, A011782, A000079, A003945, A046055, A146523, A082505, A135092.
Essentially the same as A132479, A077552, A020707.

Programs

  • Mathematica
    Join[{1},2^Range[3,40]] (* Harvey P. Dale, Feb 28 2016 *)
  • PARI
    Vec((1+6*x)/(1-2*x) + O(x^50)) \\ Colin Barker, Mar 17 2016

Formula

a(0)=1, a(n) = 2^(n+2) for n>0.
a(n) = Sum_{k, 0..n} A109466(n,k)*A146534(k).
a(n) = A132479(n), n>1. - R. J. Mathar, Nov 02 2008
G.f.: (1+6*x) / (1-2*x). - Colin Barker, Mar 17 2016

Extensions

Corrected and extended by Harvey P. Dale, Feb 28 2016

A132478 A007318^(-1) * [4*A007318^(2) - 3*A000012].

Original entry on oeis.org

1, 4, 1, 4, 11, 1, 4, 9, 18, 1, 4, 19, 15, 25, 1, 4, 17, 52, 22, 32, 1, 4, 27, 45, 110, 30, 39, 1, 4, 25, 102, 95, 200, 39, 46, 1, 4, 35, 91, 287, 175, 329, 49, 53, 1, 4, 33, 168, 252, 672, 294, 504, 60, 60, 1
Offset: 0

Views

Author

Gary W. Adamson, Aug 23 2007

Keywords

Comments

Row sums = A132479: (1, 5, 16, 32, 64, 128, 256, ...).

Examples

			First few rows of the triangle:
  1;
  4,  1;
  4, 11,  1;
  4,  9, 18,   1;
  4, 19, 15,  25,  1;
  4, 17, 52,  22, 32,  1;
  4, 27, 45, 110, 30, 39, 1;
  ...

Crossrefs

Cf. A007318, A132479.

Formula

Inverse binomial transform of [4*A007318^(2) - 3*A000012], as infinite lower triangular matrices.
Showing 1-2 of 2 results.

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