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

1,2

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.

Links

Table of n, a(n) for n=1..83.

Example

.................................... 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.

Crossrefs

Sequence in context: A346874 A348533 A089606 * A091918 A177953 A138895

Adjacent sequences: A140737 A140738 A140739 * A140741 A140742 A140743

Keyword

nonn,tabl

Author

Reinhard Zumkeller, May 26 2008

Status

approved