A140740 Triangle read by rows: T(n,n) = 1 and for k with 1 <= k < n: T(n+1,k) = T(n,k) + T(n - n mod k, k).

1, 2, 1, 4, 2, 1, 8, 3, 2, 1, 16, 6, 3, 2, 1, 32, 9, 4, 3, 2, 1, 64, 18, 8, 4, 3, 2, 1, 128, 27, 12, 5, 4, 3, 2, 1, 256, 54, 16, 10, 5, 4, 3, 2, 1, 512, 81, 32, 15, 6, 5, 4, 3, 2, 1, 1024, 162, 48, 20, 12, 6, 5, 4, 3, 2, 1, 2048, 243, 64, 25, 18, 7, 6, 5, 4, 3, 2, 1, 4096, 486, 128, 50, 24

Offset: 1

Author

Reinhard Zumkeller, May 26 2008

Keywords

• nonn
• tabl

Comments

Central terms: T(2*n-1,n)=n; T(2*n,n)=n+1; T(2*n,n+1)=n;

T(n,k) = n-k+1, for k with n/2 <= k <= n;

sums of rows: A140741;

T(n,1) = A000079(n-1);

T(n,2) = A038754(n-2) for n>1;

T(n,3) = A133464(n-3) for n>2;

T(n,4) = A140730(n-4) for n>3;

T(n,9) = A037124(n-9) for n>8.

Examples

			.................................... 1
.................................. 2 . 1
.............................. 2^2 . 2 . 1
.......................... 2^3 ... 3 . 2 . 1
...................... 2^4 ... 2*3 . 3 . 2 . 1
.................. 2^5 ... 3^2 ... 4 . 3 . 2 . 1
.............. 2^6 .. 2*3^2 .. 2*4 . 4 . 3 . 2 . 1
.......... 2^7 ... 3^3 ... 3*4 ... 5 . 4 . 3 . 2 . 1
...... 2^8 .. 2*3^3 ... 4^2 .. 2*5 . 5 . 4 . 3 . 2 . 1
... 2^9 ... 3^4 .. 2*4^2 . 3*5 ... 6 . 5 . 4 . 3 . 2 . 1
2^10 . 2*3^4 . 3*4^2 .. 4*5 .. 2*6 . 6 . 5 . 4 . 3 . 2 . 1.