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 1-1 of 1 results.

A191597 Expansion of x*(1+3*x)/ ( (1-4*x)*(1+x+x^2)).

Original entry on oeis.org

0, 1, 6, 21, 85, 342, 1365, 5461, 21846, 87381, 349525, 1398102, 5592405, 22369621, 89478486, 357913941, 1431655765, 5726623062, 22906492245, 91625968981, 366503875926, 1466015503701, 5864062014805, 23456248059222, 93824992236885, 375299968947541
Offset: 0

Views

Author

Paul Curtz, Jun 08 2011

Keywords

Comments

a(n) and successive differences define a square array T(0,k) = a(k), T(n,k) = T(n-1,k+1) - T(n-1,k):
0, 1, 6, 21, 85, 342,...
1, 5, 15, 64, 257, 1023,...
4, 10, 49, 193, 766, 3073,...
As with any sequence which obeys a homogeneous linear recurrence (we say it once, only once and we shall not repeat it), the recurrence is also valid for the rows of such arrays of higher order differences.

Programs

Formula

a(n) = 3*a(n-1) + 3*a(n-2) + 4*a(n-3), n >= 3.
a(n) = A024495(2*n).
a(n) = A113405(2*n) + A113405(2*n+1).
a(n+1) - 4*a(n) = A132677(n).
a(n+3) - a(n) = 21*4^n.
a(n) = A178872(n) + 3*A178872(n-1) = (4^n-A061347(n+1))/3. - R. J. Mathar, Jun 08 2011
Showing 1-1 of 1 results.