A128716 Triangle where the n-th row, of n terms in order, contains consecutive multiples of n. The smallest term of row n is the smallest integer greater than or equal to the largest term of row (n-1), for n >= 2.

1, 2, 4, 6, 9, 12, 12, 16, 20, 24, 25, 30, 35, 40, 45, 48, 54, 60, 66, 72, 78, 84, 91, 98, 105, 112, 119, 126, 128, 136, 144, 152, 160, 168, 176, 184, 189, 198, 207, 216, 225, 234, 243, 252, 261, 270, 280, 290, 300, 310, 320, 330, 340, 350, 360, 363, 374, 385, 396

Offset

1,2

Comments

If we instead had the triangle where the smallest term of row n is the smallest integer strictly greater than the largest term of row (n-1), for n >= 2, then we would have sequence A033291.

Links

Table of n, a(n) for n=1..59.

Formula

T(n,k+1) = T(n,k) + n for 1 <= k < n. T(n,1) = n*ceiling(T(n-1,n-1)/n) for n >= 2. - R. J. Mathar, Nov 01 2007

Example

Triangle starts
    1;
    2,   4;
    6,   9,  12;
   12,  16,  20,  24;
   25,  30,  35,  40,  45;
   48,  54,  60,  66,  72,  78;
   84,  91,  98, 105, 112, 119, 126;
  128, 136, 144, 152, 160, 168, 176, 184;
  189, 198, 207, 216, 225, 234, 243, 252, 261;

Maple

A128716 := proc(n, k) option remember ; if n = 1 then 1 ; elif k = 1 then n*ceil(A128716(n-1, n-1)/n) ; else A128716(n, k-1)+n ; fi ; end: for n from 1 to 11 do for k from 1 to n do printf("%d, ", A128716(n, k)) ; od: od: # R. J. Mathar, Nov 01 2007

Crossrefs

Cf. A033291.

Sequence in context: A237685 A220768 A077220 * A258934 A225600 A183422

Adjacent sequences: A128713 A128714 A128715 * A128717 A128718 A128719

Keyword

easy,nonn,tabl

Author

Leroy Quet, Jun 12 2007

Extensions

More terms from R. J. Mathar, Nov 01 2007

Status

approved