A093851 a(n) = A002283(n-1) + floor(A052268(n)/(1+n)).

4, 39, 324, 2799, 24999, 228570, 2124999, 19999999, 189999999, 1818181817, 17499999999, 169230769229, 1642857142856, 15999999999999, 156249999999999, 1529411764705881, 14999999999999999, 147368421052631577, 1449999999999999999, 14285714285714285713

Offset

1,1

Comments

The first column r=1 of a triangle defined by T(n,r) = 10^(n-1) -1 + r*floor(9*10^(n-1)/(n+1)).

A row starts with a (virtual) 0th column of a rep-9-digit and fills the remainder with n+1 numbers in arithmetic progression with the largest step such that all numbers in the n-th row are n-digit numbers.

Links

G. C. Greubel, Table of n, a(n) for n = 1..995

Formula

a(n) = 10^(n-1) -1 + floor(9*10^(n-1)/(n+1)). - G. C. Greubel, Apr 02 2019

Example

The triangle starts in row n=1 as
4 9 # -1, -1+5, -1+2*5
39 69 99 # 9,9+30,9+2*30
324 549 774 999 # 99, 99+225, 99+2*225, 99+3*225
2799 4599 6399 8199 9999 # 999, 999+1800, 999+2*1800,..
...
The sequence contains the first column.

Maple

A093851 := proc(n) 10^(n-1)-1+floor(9*10^(n-1)/(n+1)) ; end proc: seq(A093851(n), n=1..20) ; # R. J. Mathar, Oct 14 2010

Mathematica

Table[10^(n-1) -1 +Floor[9*10^(n-1)/(n+1)], {n, 1, 20}] (* G. C. Greubel, Apr 02 2019 *)

Prog

(PARI) {a(n) = 10^(n-1) -1 +floor(9*10^(n-1)/(n+1))}; \\ G. C. Greubel, Apr 02 2019
(Magma) [10^(n-1) -1 +Floor(9*10^(n-1)/(n+1)): n in [1..20]]; // G. C. Greubel, Apr 02 2019
(Sage) [10^(n-1) -1 +floor(9*10^(n-1)/(n+1)) for n in (1..20)] # G. C. Greubel, Apr 02 2019

Crossrefs

Cf. A061772, A093846, A093847, A093450, A093552.

Sequence in context: A360740 A059945 A198853 * A224755 A241075 A123618

Adjacent sequences: A093848 A093849 A093850 * A093852 A093853 A093854

Keyword

base,easy,nonn

Author

Amarnath Murthy, Apr 18 2004

Extensions

More terms from R. J. Mathar, Oct 14 2010

Status

approved