A133095 -id:A133095 - cp's OEIS frontend

A133094 A007318 * A133080 * A097806, as infinite lower triangular matrices.

1, 3, 1, 5, 3, 1, 7, 7, 5, 1, 9, 14, 14, 5, 1, 11, 25, 30, 16, 7, 1, 13, 41, 55, 41, 27, 7, 1, 15, 63, 91, 91, 77, 29, 9, 1, 17, 92, 140, 182, 182, 92, 44, 9, 1, 19, 129, 204, 336, 378, 246, 156, 46, 11, 1

Offset: 1

Gary W. Adamson, Sep 09 2007

Row sums give A133095.

Binomial transform of an infinite lower triangular matrix with (1,1,1,...) in the main diagonal, (2,1,2,1,...) in the subdiagonal and (0,1,0,1,...) in the subsubdiagonal.

			First few rows of the triangle:
   1;
   3,  1;
   5,  3,  1;
   7,  7,  5,  1;
   9, 14, 14,  5,  1;
  11, 25, 30, 16,  7,  1;
  13, 41, 55, 41, 27,  7,  1;
  ...

Cf. A133080, A097806, A133095.

A179744 a(0) = 1, a(n) = 3*2^(n-1) - n for n>0.

Original entry on oeis.org

1, 2, 4, 9, 20, 43, 90, 185, 376, 759, 1526, 3061, 6132, 12275, 24562, 49137, 98288, 196591, 393198, 786413, 1572844, 3145707, 6291434, 12582889, 25165800, 50331623, 100663270, 201326565, 402653156, 805306339, 1610612706, 3221225441

Offset: 0

Gary W. Adamson, Jul 25 2010

Equals row sums of triangle A179743.

Essentially the same as A133095 and A123720. - R. J. Mathar, Jul 26 2010

			a(5) = 43 = 2*a(4) + 3 = 2*20 + 3
a(5) = 43 = sum of row 5 terms, triangle A179743: (1 + 5 + 8 + 12 + 16 + 1).

Index entries for linear recurrences with constant coefficients, signature (4,-5,2).

Cf. A179743.

a[0] = 1; a[1] = 2; a[n_] := a[n] = 2 a[n - 1] + (n - 2); Array[a, 35, 0] (* Robert G. Wilson v, Aug 03 2010 *)

a(n)=3*2^n\2-n \\ Charles R Greathouse IV, May 03 2013

a(0) = 1, a(1) = 2; a(n) = 2*a(n-1) + (n-2) for n>1.

G.f. 1-x*(2-4*x+3*x^2) / ( (2*x-1)*(x-1)^2 ). - R. J. Mathar, May 03 2013

More terms from Robert G. Wilson v, Aug 03 2010

cp's OEIS Frontend

A133094 A007318 * A133080 * A097806, as infinite lower triangular matrices.

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A179744 a(0) = 1, a(n) = 3*2^(n-1) - n for n>0.

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