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A141604
Triangle, read by rows, T(n,k) = round(A006720(n)/(A006720(n-k)*A006720(k))).
2
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 1, 1, 2, 3, 3, 2, 1, 1, 2, 4, 7, 4, 2, 1, 1, 3, 8, 12, 12, 8, 3, 1, 1, 3, 8, 20, 15, 20, 8, 3, 1, 1, 5, 14, 45, 52, 52, 45, 14, 5, 1, 1, 5, 26, 66, 109, 170, 109, 66, 26, 5, 1
OFFSET
0,12
COMMENTS
The round-function in the definition is round-to-nearest, not Mathematica's round-to-even. - R. J. Mathar, Jul 12 2012
EXAMPLE
Triangle begins:
1;
1, 1;
1, 1, 1;
1, 1, 1, 1;
1, 2, 2, 2, 1;
1, 2, 3, 3, 2, 1;
1, 2, 4, 7, 4, 2, 1;
1, 3, 8, 12, 12, 8, 3, 1;
1, 3, 8, 20, 15, 20, 8, 3, 1;
1, 5, 14, 45, 52, 52, 45, 14, 5, 1;
1, 5, 26, 66, 109, 170, 109, 66, 26, 5, 1;
MAPLE
A141604 := proc(n, m)
round(A006720(n)/A006720(n-m)/A006720(m)) ;
end proc:
seq(seq(A141604(n, k), k=0..n), n=0..12) ; # R. J. Mathar, Jul 12 2012
MATHEMATICA
f[n_]:= f[n]= If[n<4, 1, (f[n-1]*f[n-3] +f[n-2]^2)/f[n-4]]; (* A006720 *)
A141604[n_, k_]:= Round[f[n]/(f[k]*f[n-k])];
Table[A141604[n, k], {n, 0, 12}, {k, 0, n}]//Flatten (* modified by G. C. Greubel, Sep 21 2024 *)
PROG
(Magma)
A006720:= [n le 4 select 1 else (Self(n-1)*Self(n-3)+Self(n-2)^2)/Self(n-4): n in [1..30]];
A141604:= func< n, k | Round(A006720[n+1]/(A006720[k+1]*A006720[n-k+1])) >;
[A141604(n, k): k in [0..n], n in [0..12]]; // G. C. Greubel, Sep 21 2024
(SageMath)
def f(n): # f = A006720
if n<4: return 1
else: return (f(n-1)*f(n-3) +f(n-2)^2)/f(n-4)
def A141604(n, k): return round(f(n)/(f(k)*f(n-k)))
flatten([[A141604(n, k) for k in range(n+1)] for n in range(13)]) # G. C. Greubel, Sep 21 2024
CROSSREFS
Cf. A006720.
Sequence in context: A134143 A295555 A085684 * A143996 A301562 A334486
KEYWORD
nonn,less,tabl
AUTHOR
STATUS
approved