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, 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.

Links

Table of n, a(n) for n=1..46.

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

Adjacent sequences: A179803 A179804 A179805 * A179807 A179808 A179809

Keyword

nonn,tabf

Author

Gary W. Adamson, Jul 28 2010

Status

approved