login
A168260
Triangle read by rows, A168258 * the diagonalized variant of A168259.
2
1, 1, 1, 2, 2, 2, 2, 2, 4, 6, 3, 3, 6, 12, 14, 3, 3, 6, 18, 28, 38, 4, 4, 8, 24, 42, 76, 96, 4, 4, 8, 24, 56, 114, 192, 254, 5, 5, 10, 30, 70, 152, 288, 508, 656, 5, 5, 10, 30, 70, 190, 384, 762, 1312, 1724, 6, 6, 12, 36, 84, 228, 480, 1016
OFFSET
1,4
COMMENTS
Row sums = A168259: (1, 2, 6, 14, 38, 96, ...).
Sum of n-th row terms = rightmost term of next row.
Conjecture: Row sum ratios tend to phi^2 = 2.6180339... (cf. A168259).
FORMULA
Let M = triangle A168258 and Q = the diagonalized variant of M's eigensequence
such that Q's rightmost diagonal = A168259 prefaced with a 1: (1, 1, 2, 6, ...).
and other terms = 0.
Triangle A168260 = M * Q as infinite lower triangular matrices.
EXAMPLE
Triangle begins:
1;
1, 1;
2, 2, 2;
2, 2, 4, 6;
3, 3, 6, 12, 14;
3, 3, 6, 18, 28, 38;
4, 4, 8, 24, 42, 76, 96;
4, 4, 8, 24, 56, 114, 192, 254;
5, 5, 10, 30, 70, 152, 288, 508, 656;
5, 5, 10, 30, 70, 190, 384, 762, 1312, 1724;
6, 6, 12, 36, 84, 228, 480, 1016, 1968, 3448, 4492;
6, 6, 12, 36, 84, 228, 576, 1270, 2624, 5172, 8984, 11776;
7, 7, 14, 42, 98, 266, 672, 1524, 3284, 6896, 13476, 23552, 30774;
7, 7, 14, 42, 98, 266, 672, 1778, 3936, 8620, 17968, 35328, 61548, 80608;
8, 8, 16, 48, 112, 304, 768, 2032, 5248, 12068, 26952, 58880, 123096, 241824;
...
CROSSREFS
Sequence in context: A175732 A327817 A353643 * A008737 A244460 A160419
KEYWORD
nonn,tabl
AUTHOR
Gary W. Adamson, Nov 21 2009
STATUS
approved