A079823 Consider the triangle shown below; sequence contains the concatenation of numbers read at a 45-degree angle upwards with horizontal beginning with the first term of a row.

1, 2, 43, 75, 1186, 16129, 22171310, 29231814, 3730241915, 4638312520, 564739322621, 675748403327, 79685849413428, 92806959504235, 10693817060514336, 121107948271615244, 137122108958372625345, 1541381231099684736354, 1721551391241109785746455

Offset: 1

Author

Amarnath Murthy, Feb 11 2003

Keywords

• base
• nonn
• changed

Comments

1

2 3

4 5 6

7 8 9 10

11 12 13 14 15

16 17 18 19 20 21

...

a(n) also is the concatenation of the terms of the n-th row of A056536. - Michel Marcus, Dec 14 2023

Links

• G. C. Greubel, Table of n, a(n) for n = 1..395

Crossrefs

Cf. A056536, A079808, A079824.

Programs

Maple

read("transforms"):
A079823aux := proc(n,k)
    A000124(n)+k ;
end proc:
A079823 := proc(n)
    local L,k,n0 ;
    n0 := n-1 ;
    L := [] ;
    for k from 0 do
        if k > n0-k then
            break;
        end if;
        L := [op(L),A079823aux(n0-k,k)] ;
    end do:
    digcatL(L) ;
end proc: # R. J. Mathar, Aug 23 2012
# second Maple program:
T:= (i, j)-> i*(i-1)/2+j:
a:= n-> parse(cat(seq(T(n-j,j+1), j=0..(n-1)/2))):
seq(a(n), n=1..23);  # Alois P. Heinz, Aug 03 2022

Mathematica

Table[FromDigits[Join@@IntegerDigits[Table[Binomial[n-k+1,2] + k, {k, Ceiling[n/2]}]]], {n,30}] (* G. C. Greubel, Dec 13 2023 *)

Extensions

More terms from Jason D. W. Taff (jtaff(AT)jburroughs.org), Oct 31 2003

Corrected by Philippe Deléham, Feb 16 2004