A179901 Triangle read by rows, antidiagonals of an array generated from (1, r, r, r, ...) convolved with (1, 0, r, r, r, ...).

1, 1, 1, 1, 2, 2, 1, 3, 4, 3, 1, 4, 6, 8, 4, 1, 5, 8, 15, 12, 5, 1, 6, 10, 24, 24, 16, 6, 1, 7, 12, 35, 40, 33, 20, 7, 1, 8, 14, 48, 60, 56, 42, 24, 8, 1, 9, 16, 63, 84, 85, 70, 51, 28, 9, 1, 10, 18, 80, 112, 120, 110, 88, 60, 32, 10, 1, 11, 20, 99, 144, 161, 156, 135, 104, 69, 36, 11

Offset: 1

Author

Gary W. Adamson, Jul 31 2010

Keywords

• nonn
• tabl

Comments

Row sums = A179902: (1, 2, 5, 11, 23, 46, 87, 155, ...).

Examples

			First few rows of the array:
.
1,.1,..2,...3,...4,...5,...6,...7,....8,...
1,.2,..4,...8,..12,..16...20,..24,...28,... = A019442
1,.3,..6,..15,..24,..33,..42,..51,...60,... = A179805
1,.4,..8,..24,..40,..56,..70,..88,..104,...
.
Example: row 4 = (1, 4, 8, 24, ...) = (1, 4, 4, 4, ...) * (1, 0, 4, 4, 4, ...) = (1, r, 2*r, (2*r + r^2), ...).
.
First few rows of the triangle:
.
1,
1, 1;
1, 2, 2;
1, 3, 4, 3;
1, 4, 6, 8, 4;
1, 5, 8, 15, 12, 5;
1, 6, 10, 24, 24, 16, 6;
1, 7, 12, 35, 40, 33, 20, 7;
1, 8, 14, 48, 60, 56, 42, 24, 8;
1, 9, 16, 63, 84, 85, 70, 51, 28, 9;
1, 10, 18, 80, 112, 120, 110, 88, 60, 32, 10;
1, 11, 20, 99, 144, 161, 156, 135, 104, 69, 36, 11;
1, 12, 22, 120, 180, 208, 210, 192, 160, 120, 78, 40, 12;
1, 13, 24, 143, 220, 261, 272, 259, 228, 185, 136, 87, 44, 13;
...
		

Crossrefs

Cf. A019442, A179805

Formula

Triangle read by rows, antidiagonals of an array generated from (1, r, r, r, ...) convolved with (1, 0, r, r, r, ...), such that the r-th row of the array = (1, r, 2*r, ...) then for n > 3, a(n) = r^2 + a(n-1).