A093846 Triangle read by rows: T(n, k) = 10^(n-1) - 1 + k*floor(9*10^(n-1)/n), for 1 <= k <= n.

9, 54, 99, 399, 699, 999, 3249, 5499, 7749, 9999, 27999, 45999, 63999, 81999, 99999, 249999, 399999, 549999, 699999, 849999, 999999, 2285713, 3571427, 4857141, 6142855, 7428569, 8714283, 9999997, 21249999, 32499999, 43749999, 54999999, 66249999, 77499999, 88749999, 99999999

Offset

1,1

Comments

10^(n-1)-1 and the n-th row are n+1 numbers in arithmetic progression and the common difference is the largest such that a(n, n) has n digits. This common difference equals A061772(n).

Links

G. C. Greubel, Rows n = 1..100 of triangle, flattened

Example

Triangle begins:
     9;
    54,   99;
   399,  699,  999;
  3249, 5499, 7749, 9999;
  ...

Maple

A093846 := proc(n, k) RETURN (10^(n-1)-1+k*floor(9*(10^(n-1)/n))); end; for n from 1 to 10 do for k from 1 to n do printf("%d, ", A093846(n, k)); od; od; # R. J. Mathar, Jun 23 2006

Mathematica

Table[# -1 +k Floor[9 #/n] &[10^(n-1)], {n, 8}, {k, n}]//Flatten (* Michael De Vlieger, Jul 18 2016 *)

Prog

(PARI) {T(n, k) = 10^(n-1) -1 +k*floor(9*10^(n-1)/n)}; \\ G. C. Greubel, Mar 22 2019
(Magma) [[10^(n-1) -1 +k*Floor(9*10^(n-1)/n): k in [1..n]]: n in [1..8]]; // G. C. Greubel, Mar 22 2019
(Sage) [[10^(n-1) -1 +k*floor(9*10^(n-1)/n) for k in (1..n)] for n in (1..8)] # G. C. Greubel, Mar 22 2019

Crossrefs

Cf. A061772, A093847, A093849, A093850.

Sequence in context: A259316 A224484 A225791 * A152994 A034719 A013567

Adjacent sequences: A093843 A093844 A093845 * A093847 A093848 A093849

Keyword

base,easy,less,nonn,tabl

Author

Amarnath Murthy, Apr 18 2004

Extensions

Corrected and extended by R. J. Mathar, Jun 23 2006

Edited by David Wasserman, Mar 26 2007

Status

approved