A133805 -id:A133805 - cp's OEIS frontend

A131051 Row sums of triangle A133805.

1, 3, 8, 18, 38, 78, 158, 318, 638, 1278, 2558, 5118, 10238, 20478, 40958, 81918, 163838, 327678, 655358, 1310718, 2621438, 5242878, 10485758, 20971518, 41943038, 83886078, 167772158, 335544318, 671088638, 1342177278, 2684354558

Offset: 1

Gary W. Adamson, Sep 23 2007

Last digit of a(n) is 8 for n > 2. - Jon Perry, Nov 19 2012

			a(4) = 18 = sum of row 4 terms of triangle A133805: (7 + 6 + 4 + 1).
a(4) = 18 = (1, 3, 3, 1), dot (1, 2, 3, 2) = (1 + 6 + 9 + 2).

Essentially a duplicate of A051633.
Cf. A133805.
Cf. A083329, A053209.

a:=[1]; for n in [2..31] do Append(~a,2*n-2+&+[a[i]:i in [1..n-1]]); end for; a; // Marius A. Burtea, Oct 15 2019

R:=PowerSeriesRing(Integers(), 31); Coefficients(R!( (1+x^2)/((1-x)*(1-2*x)))); // Marius A. Burtea, Oct 15 2019

Binomial transform of [1, 2, 3, 2, 3, 2, 3, ...].
O.g.f.: (1+x^2)/((1-x)(1-2*x)). a(n)=A051633(n-2). - R. J. Mathar, Jun 13 2008
a(n) = 5*2^(n-2)-2, n>1. - Gary Detlefs, Jun 22 2010
a(n) = 2(n-1) + Sum_{i=1..n-1} a(i). - Jon Perry, Nov 19 2012

More terms from R. J. Mathar, Jun 13 2008

A133804 Triangle read by rows: A007318 * A133080 * A133566.

Original entry on oeis.org

1, 2, 1, 3, 3, 1, 4, 7, 4, 1, 5, 14, 10, 5, 1, 6, 25, 20, 16, 6, 1, 7, 41, 35, 41, 21, 7, 1, 8, 63, 56, 91, 56, 29, 8, 1, 9, 92, 84, 182, 126, 92, 36, 9, 1, 10, 129, 120, 336, 252, 246, 120, 46, 10, 1, 11, 175, 165, 582, 462, 582, 330, 175, 55, 11, 1, 12, 231, 220, 957, 792, 1254, 792, 550, 220, 67, 12, 1

Offset: 1

Gary W. Adamson, Sep 23 2007

Row sums = A133124: (1, 3, 7, 16, 35, 74, 153, ...).

A133805 = binomial transform of (A133566 * A133080).

			First few rows of the triangle:
  1;
  2,  1;
  3,  3,  1;
  4,  7,  4,  1;
  5, 14, 10,  5,  1;
  6, 25, 20, 16,  6,  1;
  7, 41, 35, 41, 21,  7,  1;
  ...

Cf. A133080, A133124, A133566.

Binomial transform of (A133080 * A133566), where A133080 * A133566 = an infinite lower triangular matrix with (1,1,1,...) in the main and subdiagonals and (0,1,0,1,0,...) in the subsubdiagonal.

a(21) = 1 inserted and more terms from Georg Fischer, Jun 08 2023

cp's OEIS Frontend

A131051 Row sums of triangle A133805.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Magma