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A107449 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.

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