%I #19 Feb 19 2025 16:12:30
%S 5,3,9,3,7,3,7,9,9,7,3,7,9,1,7,1,3,3,1,7,1,3,3,1,7,1,3,3,7,3,7,9,9,7,
%T 3,7,9,9,7,3,7,9,9,7,3,7,9,9,7,3,7,9,9,7,3,7,9,9,7,3,7,9,9,7,3,7,9,3,
%U 9,3,5,5,3,9,3,5,5,3,9,3,5,5,3,9,3,5,5,3,9,3,5,5,3,9,3,5,5,3,9,3,5,5,3,9,3
%N Irregular triangle T(n, k) = 10 - ( (b(n) + k^2 + k + 1) mod 10 ), where b(n) = A056486(n-1) - (1/2)*[n=1], for n >= 1 and 1 <= k <= b(n) - 1, read by rows.
%H G. C. Greubel, <a href="/A107449/b107449.txt">Table of n, a(n) for n = 1..2206</a>
%F T(n, k) = 10 - (b(n) + k^2 + k + 1) mod 10, where b(n) = A056486(n-1) - (1/2)*[n=1], for n >= 1 and 1 <= k <= b(n) - 1. - _G. C. Greubel_, Mar 24 2024
%e The irregular triangle begins as:
%e 5;
%e 3, 9, 3;
%e 7, 3, 7, 9, 9, 7, 3, 7, 9;
%e 1, 7, 1, 3, 3, 1, 7, 1, 3, 3, 1, 7, 1, 3, 3;
%t b[n_]:= 2^(n-3)*(9-(-1)^n) -Boole[n==1]/2;
%t T[n_, k_]:= 10 -Mod[k^2+k+1+b[n], 10];
%t Table[T[n, k], {n,8}, {k,b[n]-1}]//Flatten (* _G. C. Greubel_, Mar 24 2024 *)
%o (Magma)
%o b:= func< n | n eq 1 select 2 else 2^(n-3)*(9-(-1)^n) >;
%o A107448:= func< n, k | 10 - ((b(n) +k^2 +k +1) mod 10) >;
%o [5,3,9,3] cat [A107448(n, k): k in [1..b(n)-1], n in [3..8]]; // _G. C. Greubel_, Mar 24 2024
%o (SageMath)
%o def b(n): return 2^(n-3)*(9-(-1)^n) - int(n==1)/2
%o def A107449(n, k): return 10 - ((b(n) + k^2+k+1)%10);
%o flatten([[A107449(n, k) for k in range(1, b(n))] for n in range(1, 8)]) # _G. C. Greubel_, Mar 24 2024
%Y Cf. A056486, A082605.
%K nonn,tabf,less,changed
%O 1,1
%A _Roger L. Bagula_, May 26 2005
%E Edited by _G. C. Greubel_, Mar 24 2024