A290347 Numerators of the Harary index for the n-halved cube graph.

0, 1, 6, 26, 100, 1096, 3920, 13936, 16544, 296256, 1068672, 11652352, 42658304, 1100471296, 4079876096, 15205967872, 56939270144, 642281037824, 2423854317568, 9177027411968, 34846713511936, 1459319692460032, 5568939824513024, 21297365878571008

Offset

1,3

Comments

For p > 3, if p is prime, then p^2 divides a(p). Conjecture: for n > 3, if n^2 divides a(n), then n is prime. Primes p such that p^3 diviedes a(p) are probably A088164. - Thomas Ordowski, Mar 30 2025

Links

Table of n, a(n) for n=1..24.

Eric Weisstein's World of Mathematics, Harary Index

Eric Weisstein's World of Mathematics, Halved Cube Graph

Formula

a(n) = -2^(n-1)*HarmonicNumber(n)-2^(2*n-1)*Re(LerchPhi(2,1,n+1)).

For n > 1, A000265(a(n)) = A330718(n). - Thomas Ordowski, Mar 30 2025

Example

First few terms are 0, 1, 6, 26, 100, 1096/3, 3920/3, 13936/3, 16544, 296256/5, ....

Mathematica

Table[-2^(n - 1) HarmonicNumber[n] - 2^(2 n - 1) Re[LerchPhi[2, 1, n + 1]], {n, 20}] // Numerator

Crossrefs

Cf. A000265, A088164, A290348 (denominators), A330718.

Sequence in context: A005022 A125107 A301476 * A034560 A307306 A143955

Adjacent sequences: A290344 A290345 A290346 * A290348 A290349 A290350

Keyword

nonn,frac

Author

Eric W. Weisstein, Jul 28 2017

Status

approved