OFFSET
1,2
COMMENTS
Row sums give A000292, starting (1, 4, 10, 20, 35, 56, 84, ...).
FORMULA
Regarded as an array by antidiagonals A(i, j) = degree in q of q-Fibonacci number F(i+2, j-1) where F(1, k) = F(2, k) = 1, F(n, k) = F(n-1, k) + q^(n+k-2) * F(n-2, k). - Michael Somos, Jun 08 2011
EXAMPLE
First few rows of the triangle are:
1;
2, 2;
4, 3, 3;
6, 6, 4, 4;
9, 8, 8, 5, 5;
12, 12, 10, 10, 6, 6;
16, 15, 15, 12, 12, 7, 7;
...
First few rows of the array are:
1, 2, 3, 4, 5, 6, 7, 8, ...
2, 3, 4, 5, 6, 7, 8, 9, ...
4, 6, 8, 10, 12, 14, 16, 18, ...
6, 8, 10, 12, 14, 16, 18, 20, ...
9, 12, 15, 18, 21, 24, 27, 30, ...
...
A(3, 4) = 10 because F(5, 3) = 1 + q^4 + q^5 + q^6 + q^10. A(4, 4) = 12 because F(6, 3) = 1 + q^4 + q^5 + q^6 + q^7 + q^10 + q^11 + q^12.
PROG
(PARI) {T(n, k) = (n - k + 2)\2 * ((n + k + 1)\2)} /* Michael Somos, Jun 08 2011 */
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Gary W. Adamson, Mar 11 2007
EXTENSIONS
a(19) = 10 inserted and more terms from Georg Fischer, Jun 08 2023
STATUS
approved