A158841 Triangle read by rows, matrix product of A145677 * A004736.

1, 3, 1, 7, 4, 2, 13, 9, 6, 3, 21, 16, 12, 8, 4, 31, 25, 20, 15, 10, 5, 43, 36, 30, 24, 18, 12, 6, 57, 49, 42, 35, 28, 21, 14, 7, 73, 64, 56, 48, 40, 32, 24, 16, 8, 91, 81, 72, 63, 54, 45, 36, 27, 18, 9

Offset: 1

Author

Gary W. Adamson and Roger L. Bagula, Mar 28 2009

Keywords

• nonn
• tabl
• easy

Examples

			First few rows of the triangle:
    1;
    3,   1;
    7,   4,   2;
   13,   9,   6,   3;
   21,  16,  12,   8,   4;
   31,  25,  20,  15,  10,  5;
   43,  36,  30,  24,  18, 12,  6;
   57,  49,  42,  35,  28, 21, 14,  7;
   73,  64,  56,  48,  40, 32, 24, 16,  8;
   91,  81,  72,  63,  54, 45, 36, 27, 18,  9;
  111, 100,  90,  80,  70, 60, 50, 40, 30, 20, 10;
  133, 121, 110,  99,  88, 77, 66, 55, 44, 33, 22, 11;
  157, 144, 132, 120, 108, 96, 84, 72, 60, 48, 36, 24, 12;
  ...
		

Crossrefs

Cf. A145677, A002061 (column k=1), A158842 (row sums).

Programs

Maple

A145677 := proc(n,k)
        if n <0 or k < 0 or k > n then
                0;
        elif k = 0 then
                1;
        elif k = n then
                n ;
        else
                0 ;
        end if;
end proc:
A004736 := proc(n,k)
        if n <0 or k < 1 or k > n then
                0;
        else
                n-k+1 ;
        end if;
end proc:
A158841 := proc(n,k)
        add( A145677(n-1,j-1)*A004736(j,k),j=k..n) ;
end proc: # R. J. Mathar, Nov 05 2011

Formula

T(n,k) = Sum_{j=k..n} A145677(n-1,j-1)*A004736(j,k), assuming column enumeration k >= 1 in A004736. - R. J. Mathar, Nov 05 2011