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.

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, 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, 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

Offset: 1

Author

Roger L. Bagula, May 26 2005

Keywords

• nonn
• tabf
• less

Examples

			The irregular triangle begins as:
  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;
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..2206

Crossrefs

Cf. A056486, A082605.

Programs

Magma

b:= func< n | n eq 1 select 2 else 2^(n-3)*(9-(-1)^n) >;
A107448:= func< n, k | 10 - ((b(n) +k^2 +k +1) mod 10) >;
[5,3,9,3] cat [A107448(n, k): k in [1..b(n)-1], n in [3..8]]; // G. C. Greubel, Mar 24 2024

Mathematica

b[n_]:= 2^(n-3)*(9-(-1)^n) -Boole[n==1]/2;
T[n_, k_]:= 10  -Mod[k^2+k+1+b[n], 10];
Table[T[n, k], {n,8}, {k,b[n]-1}]//Flatten (* G. C. Greubel, Mar 24 2024 *)

SageMath

def b(n): return 2^(n-3)*(9-(-1)^n) - int(n==1)/2
def A107449(n, k): return 10 - ((b(n) + k^2+k+1)%10);
flatten([[A107449(n, k) for k in range(1, b(n))] for n in range(1, 8)]) # G. C. Greubel, Mar 24 2024

Formula

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

Extensions

Edited by G. C. Greubel, Mar 24 2024