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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.
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%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