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A179806
Irregular triangle by rows, M*Q. M = triangle with (1,2,3,...) in every column, with the leftmost column shifted upwards one row. Q = a diagonalized variant of odd-indexed Fibonacci numbers.
1
1, 2, 3, 2, 4, 4, 5, 5, 6, 10, 13, 6, 8, 15, 26, 34, 7, 10, 20, 39, 68, 89, 8, 12, 25, 52, 102, 178, 233, 9, 14, 30, 65, 136, 267, 466, 610, 10, 16, 35, 78, 170, 356, 699, 1220, 1597
OFFSET
1,2
COMMENTS
Row sums = the odd-indexed Fibonacci numbers, A001519, starting with offset 1.
Sums of row terms = (1, 2, 5, 13, 34, 89, ...).
For rows > 1, sum of n-th row terms = rightmost term of next row.
FORMULA
Triangle, M*Q; where M = a triangle with (1,2,3,...) in every column with the leftmost column shifted upwards one row. Q = an infinite matrix with the odd-indexed Fibonacci numbers as the right border: (1, 2, 5, 13,...) and
the rest zeros.
EXAMPLE
First few rows of the triangle:
1;
2;
3, 2;
4, 4, 5;
5, 6, 10, 13;
6, 8, 15, 26, 34;
7, 10, 20, 39, 68, 89;
8, 12, 25, 52, 102, 178, 233;
9, 14, 30, 65, 136, 267, 466, 610;
10, 16, 35, 78, 170, 356, 699, 1220, 1597;
11, 18, 40, 91, 204, 445, 932, 1830, 3194, 4181;
12, 20, 45, 104, 238, 534, 1165, 2440, 4791, 8362, 10946;
...
CROSSREFS
Cf. A001519.
Sequence in context: A320348 A336315 A145394 * A364346 A182762 A173997
KEYWORD
nonn,tabf
AUTHOR
Gary W. Adamson, Jul 28 2010
STATUS
approved