OFFSET
1,2
COMMENTS
a(n) equals the largest term in row n of triangle A110205.
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..825
FORMULA
a(n) = (8^n-1)/7*C(n-3, floor(n/2)) + ((2^n-1)*(4^n-1)-(8^n-1)/7)*C(n-3, floor(n/2)-1) + (2^n-1)^3*C(n-3, floor(n/2)-2).
MATHEMATICA
b[n_, k_]:= Binomial[n-3, Floor[n/2]-k];
f[n_]:= (8^n-1)/7*(b[n, 0] - b[n, 1]) + (2^n-1)^2*((2^n+1)*b[n, 1] + (2^n - 1)*b[n, 2]);
A110207[n_]:= If[n<3, f[n]/2, f[n]];
Table[A110207[n], {n, 30}] (* G. C. Greubel, Oct 03 2024 *)
PROG
(PARI) {a(n)=(8^n-1)/7*binomial(n-3, n\2)+((2^n-1)*(4^n-1)-(8^n-1)/7)*binomial(n-3, n\2-1) +(2^n-1)^3*binomial(n-3, n\2-2)}
(Magma)
b:= func< n, k | Binomial(n-3, Floor(n/2) - k) >;
A110207:= func< n | (8^n-1)/7*(b(n, 0) - b(n, 1)) + (2^n-1)^2*((2^n+1)*b(n, 1) + (2^n-1)*b(n, 2)) >;
[A110207(n): n in [1..30]]; // G. C. Greubel, Oct 03 2024
(SageMath)
def b(n, k): return binomial(n-3, (n//2) - k)
def A110207(n): return (8^n-1)/7*(b(n, 0) - b(n, 1)) + (2^n-1)^2*((2^n+1)*b(n, 1) + (2^n-1)*b(n, 2))
[A110207(n) for n in range(1, 31)] # G. C. Greubel, Oct 03 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jul 16 2005
STATUS
approved