A128590 Triangle read by rows, matrix product A128179 * A000012.
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, 20, 20, 18, 18, 14, 14, 8, 8, 25, 24, 24, 21, 21, 16, 16, 9, 9, 30, 30, 28, 28, 24, 24, 18, 18, 10, 10, 36, 35, 35, 32, 32, 27, 27, 20, 20, 11, 11, 42, 42, 40, 40, 36, 36, 30, 30, 22, 22, 12, 12
Offset: 1
Examples
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.
Programs
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PARI
{T(n, k) = (n - k + 2)\2 * ((n + k + 1)\2)} /* Michael Somos, Jun 08 2011 */
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
Extensions
a(19) = 10 inserted and more terms from Georg Fischer, Jun 08 2023
Comments