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Triangular array read by rows: T(n,k) = k*floor(n/10) + n mod 10, 0<=k<=n.
2

%I #12 May 23 2024 16:12:50

%S 0,1,1,2,2,2,3,3,3,3,4,4,4,4,4,5,5,5,5,5,5,6,6,6,6,6,6,6,7,7,7,7,7,7,

%T 7,7,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,0,1,2,3,4,5,6,7,8,9,10,1,2,

%U 3,4,5,6,7,8,9,10,11,12,2,3,4,5,6,7,8,9,10,11,12,13,14,3,4,5,6,7,8,9,10,11

%N Triangular array read by rows: T(n,k) = k*floor(n/10) + n mod 10, 0<=k<=n.

%C A010879(n)=T(n,0);

%C A076314(0)=T(0,0), A076314(n)=T(n,1) for n>0;

%C A028897(n)=T(n,n) for n<=1, A028897(n)=T(n,2) for n>1;

%C A028898(n)=T(n,n) for n<=2, A028898(n)=T(n,3) for n>2;

%C A028899(n)=T(n,n) for n<=3, A028899(n)=T(n,4) for n>3;

%C A028900(n)=T(n,n) for n<=4, A028900(n)=T(n,5) for n>4;

%C A028901(n)=T(n,n) for n<=5, A028901(n)=T(n,6) for n>5;

%C A028902(n)=T(n,n) for n<=6, A028902(n)=T(n,7) for n>6;

%C A028903(n)=T(n,n) for n<=7, A028903(n)=T(n,8) for n>7;

%C A028904(n)=T(n,n) for n<=8, A028904(n)=T(n,9) for n>8;

%C T(n,n) = n for n<=9, T(n,10) = n for n>9;

%C A083292(n) = T(n,n).

%H Paolo Xausa, <a href="/A083291/b083291.txt">Table of n, a(n) for n = 0..11475</a> (rows 0..150 of the triangle, flattened).

%e From _Paolo Xausa_, May 22 2024: (Start)

%e Triangle begins:

%e [0] 0;

%e [1] 1, 1;

%e [2] 2, 2, 2;

%e [3] 3, 3, 3, 3;

%e [4] 4, 4, 4, 4, 4;

%e [5] 5, 5, 5, 5, 5, 5;

%e [6] 6, 6, 6, 6, 6, 6, 6;

%e [7] 7, 7, 7, 7, 7, 7, 7, 7;

%e [8] 8, 8, 8, 8, 8, 8, 8, 8, 8;

%e [9] 9, 9, 9, 9, 9, 9, 9, 9, 9, 9;

%e [10] 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10;

%e ... (End)

%t Table[k*Floor[n/10] + Mod[n, 10], {n, 0, 10}, {k, 0, n}]//Flatten (* _Paolo Xausa_, May 22 2024 *)

%K nonn,tabl

%O 0,4

%A _Reinhard Zumkeller_, Apr 23 2003

%E Offset changed to 0 by _Paolo Xausa_, May 22 2024