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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.

%I A079823 #24 Aug 27 2025 21:20:14
%S A079823 1,2,43,75,1186,16129,22171310,29231814,3730241915,4638312520,
%T A079823 564739322621,675748403327,79685849413428,92806959504235,
%U A079823 10693817060514336,121107948271615244,137122108958372625345,1541381231099684736354,1721551391241109785746455
%N 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.
%C A079823    1
%C A079823    2  3
%C A079823    4  5  6
%C A079823    7  8  9 10
%C A079823   11 12 13 14 15
%C A079823   16 17 18 19 20 21
%C A079823   ...
%C A079823 a(n) also is the concatenation of the terms of the n-th row of A056536. - _Michel Marcus_, Dec 14 2023
%H A079823 G. C. Greubel, <a href="/A079823/b079823.txt">Table of n, a(n) for n = 1..395</a>
%p A079823 read("transforms"):
%p A079823 A079823aux := proc(n,k)
%p A079823     A000124(n)+k ;
%p A079823 end proc:
%p A079823 A079823 := proc(n)
%p A079823     local L,k,n0 ;
%p A079823     n0 := n-1 ;
%p A079823     L := [] ;
%p A079823     for k from 0 do
%p A079823         if k > n0-k then
%p A079823             break;
%p A079823         end if;
%p A079823         L := [op(L),A079823aux(n0-k,k)] ;
%p A079823     end do:
%p A079823     digcatL(L) ;
%p A079823 end proc: # _R. J. Mathar_, Aug 23 2012
%p A079823 # second Maple program:
%p A079823 T:= (i, j)-> i*(i-1)/2+j:
%p A079823 a:= n-> parse(cat(seq(T(n-j,j+1), j=0..(n-1)/2))):
%p A079823 seq(a(n), n=1..23);  # _Alois P. Heinz_, Aug 03 2022
%t A079823 Table[FromDigits[Join@@IntegerDigits[Table[Binomial[n-k+1,2] + k, {k, Ceiling[n/2]}]]], {n,30}] (* _G. C. Greubel_, Dec 13 2023 *)
%Y A079823 Cf. A056536, A079808, A079824.
%K A079823 base,nonn,changed
%O A079823 1,2
%A A079823 _Amarnath Murthy_, Feb 11 2003
%E A079823 More terms from Jason D. W. Taff (jtaff(AT)jburroughs.org), Oct 31 2003
%E A079823 Corrected by _Philippe Deléham_, Feb 16 2004