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
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; ...
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).
Comments