A296191 Numerators of the Harary index of the n X n grid graph.

0, 5, 133, 293, 3399, 137111, 140351, 4854401, 18690167, 94423807, 2190046361, 11026443655, 11090909287, 323238388599, 4312895221021, 8658059232167, 60805695015569, 2256364094708093, 2262227096103773, 92967638570454913

Offset

1,2

Links

Table of n, a(n) for n=1..20.

Eric Weisstein's World of Mathematics, Grid Graph

Eric Weisstein's World of Mathematics, Harary Index

Example

0, 5, 133/6, 293/5, 3399/28, 137111/630, 140351/396, ...

Mathematica

Table[n (2 n + 1) (2 + (2 n - 1) Derivative[1][Log[CatalanNumber[# - 1]] &][n] - n)/3, {n, 20}] // FullSimplify // Numerator
Table[n (2 n + 1) (2 + (2 n - 1) (HarmonicNumber[n - 3/2] - HarmonicNumber[n] + 2 Log[2]) - n)/3, {n, 20}] // FunctionExpand // FullSimplify // Numerator

Crossrefs

Cf. A296192 (denominators).

Sequence in context: A135758 A152794 A053517 * A114474 A344395 A280305

Adjacent sequences: A296188 A296189 A296190 * A296192 A296193 A296194

Keyword

nonn,frac

Author

Eric W. Weisstein, Dec 07 2017

Status

approved