A134234 Triangle read by rows, n-th row = n terms of 2n, 2n+2, 2n+4, ..., 1; with a(1) = 1.

1, 4, 1, 6, 8, 1, 8, 10, 12, 1, 10, 12, 14, 16, 1, 12, 14, 16, 18, 20, 1, 14, 16, 18, 20, 22, 24, 1, 16, 18, 20, 22, 24, 26, 28, 1, 18, 20, 22, 24, 26, 28, 30, 32, 1, 20, 22, 24, 26, 28, 30, 32, 34, 36, 1

Offset

1,2

Comments

Row sums = A056108: (1, 5, 15, 31, 53, ...).

Links

Robert Israel, Table of n, a(n) for n = 1..10011

Formula

G.f.: 2*x/(1-x)^2 - 2*(2-x)/(1-x)*Sum_{n>=1} n*x^(n*(n+1)/2) + (3-x)/(1-x)*Sum_{n>=1} x^(n*(n+1)/2). - Robert Israel, Jan 15 2016

Example

First few rows of the triangle:
   1;
   4,  1;
   6,  8,  1;
   8, 10, 12,  1;
  10, 12, 14, 16, 1;
  ...

Maple

seq(op([seq(2*n+2*k, k=0..n-2), 1]), n=1..10); # Robert Israel, Jan 15 2016

Mathematica

Flatten[Table[Join[{1}, Range[n, 2n-3, 2]], {n, 4, 30, 2}]] (* Harvey P. Dale, Nov 06 2013 *)

Crossrefs

Cf. A056108.

Sequence in context: A214561 A066575 A070251 * A207628 A350106 A205137

Adjacent sequences: A134231 A134232 A134233 * A134235 A134236 A134237

Keyword

nonn,tabl

Author

Gary W. Adamson, Oct 14 2007

Status

approved