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

1,2

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

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
# Alternative:
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 *)

Crossrefs

Cf. A056536, A079808, A079824.

Sequence in context: A137415 A090194 A107200 * A107156 A062582 A073594

Adjacent sequences: A079820 A079821 A079822 * A079824 A079825 A079826

Keyword

base,nonn

Author

Amarnath Murthy, Feb 11 2003

Extensions

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

Corrected by Philippe Deléham, Feb 16 2004

Status

approved