A110207 a(n) = sum of cubes of numbers < 2^n having exactly [n/2]+1 ones in their binary expansion.

1, 27, 368, 6615, 88536, 1449198, 20078192, 320944275, 4584724120, 72867715074, 1064153845776, 16896536592390, 250629464211504, 3980364331323996, 59709362473177824, 948742244639103915, 14352114907032903000

Offset

1,2

Comments

a(n) equals the largest term in row n of triangle A110205.

Links

Table of n, a(n) for n=1..17.

Formula

a(n) = (8^n-1)/7*C(n-3, [n/2]) + ((2^n-1)*(4^n-1)-(8^n-1)/7)*C(n-3, [n/2]-1) + (2^n-1)^3*C(n-3, [n/2]-2).

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)}

Crossrefs

Cf. A110205 (triangle), A110206 (row sums).

Sequence in context: A223278 A278091 A042410 * A223205 A257786 A161530

Adjacent sequences: A110204 A110205 A110206 * A110208 A110209 A110210

Keyword

nonn

Author

Paul D. Hanna, Jul 16 2005

Status

approved