A177696 A symmetrical triangle from the generalization of A051597:m=2;a(n,k)=m*a(n - 1, k - 1) + m*a(n - 1, k)

1, 2, 2, 3, 8, 3, 4, 22, 22, 4, 5, 52, 88, 52, 5, 6, 114, 280, 280, 114, 6, 7, 240, 788, 1120, 788, 240, 7, 8, 494, 2056, 3816, 3816, 2056, 494, 8, 9, 1004, 5100, 11744, 15264, 11744, 5100, 1004, 9, 10, 2026, 12208, 33688, 54016, 54016, 33688, 12208, 2026, 10

Offset

1,2

Comments

Row sums are:

{1, 4, 14, 52, 202, 800, 3190, 12748, 50978, 203896,...].

The leading ones adjusted form a(n,k)-a(n,1)+1 gives of A051597:

{1},

{1, 1},

{1, 2, 1},

{1, 4, 4, 1},

{1, 7, 10, 7, 1},...

Of this sequence it is:

{1},

{1, 1},

{1, 6, 1},

{1, 19, 19, 1},

{1, 48, 84, 48, 1},...

Links

Table of n, a(n) for n=1..55.

Formula

m=2;

a(n,k)=m*a(n - 1, k - 1) + m*a(n - 1, k)

Example

{1},
{2, 2},
{3, 8, 3},
{4, 22, 22, 4},
{5, 52, 88, 52, 5},
{6, 114, 280, 280, 114, 6},
{7, 240, 788, 1120, 788, 240, 7},
{8, 494, 2056, 3816, 3816, 2056, 494, 8},
{9, 1004, 5100, 11744, 15264, 11744, 5100, 1004, 9},
{10, 2026, 12208, 33688, 54016, 54016, 33688, 12208, 2026, 10}

Mathematica

Clear[A, n, k, m]
m = 2;
A[n_, 1] := n;
A[n_, n_] := n;
A[n_, k_] := A[n, k] = m*A[n - 1, k - 1] + m*A[n - 1, k];
A[1, 1] := 1;
b = Table[A[n, k], {n, 10}, {k, n}];
TableForm[%];
Flatten[b]

Crossrefs

Cf. A051597

Sequence in context: A145596 A186753 A135835 * A134574 A141617 A267644

Adjacent sequences: A177693 A177694 A177695 * A177697 A177698 A177699

Keyword

nonn,tabl,uned

Author

Roger L. Bagula, May 11 2010

Status

approved