A107661 Array read by antidiagonals: T(n,m) = Sum m^max(k,n-k),k=0..n.

1, 1, 2, 1, 4, 3, 1, 6, 10, 4, 1, 8, 21, 24, 5, 1, 10, 36, 72, 52, 6, 1, 12, 55, 160, 225, 112, 7, 1, 14, 78, 300, 656, 702, 232, 8, 1, 16, 105, 504, 1525, 2688, 2133, 480, 9, 1, 18, 136, 784, 3060, 7750, 10816, 6480, 976, 10, 1, 20, 171, 1152, 5537, 18576, 38875

Offset

0,3

Links

Table of n, a(n) for n=0..61.

Formula

a(2n) = m^n(2(m^(n+1)-1)/(m-1)-1), a(2n+1) = 2m^(n+1)(m^(n+1)-1)/(m-1)

T(5,m) = m^2*(2*m^2+2*m+1). - R. J. Mathar, Aug 16 2013

Example

The array starts in row n=0 and column m=1 as:
    1,    1,    1,    1,    1,    1,...
    2,    4,    6,    8,   10,   12,...
    3,   10,   21,   36,   55,   78,...
    4,   24,   72,  160,  300,  504,...
    5,   52,  225,  656, 1525, 3060,...
    6,  112,  702, 2688, 7750,18576,...
    7,  232, 2133,10816,38875,111672,...
    8,  480, 6480,43520,195000,671328,...

Crossrefs

Cf. A107659, A107660, A014105 (3rd row), A181617 (4th row)

Sequence in context: A094437 A172431 A053123 * A126570 A048790 A027421

Adjacent sequences: A107658 A107659 A107660 * A107662 A107663 A107664

Keyword

nonn,easy,tabl

Author

Mitch Harris

Status

approved