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

1,1

Links

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

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

Example

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;

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 *)

Prog

(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
(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

Crossrefs

Cf. A056486, A082605.

Sequence in context: A073243 A134943 A105372 * A155496 A128426 A336057

Adjacent sequences: A107446 A107447 A107448 * A107450 A107451 A107452

Keyword

nonn,less

Author

Roger L. Bagula, May 26 2005

Extensions

Edited by G. C. Greubel, Mar 24 2024

Status

approved