A152086 a(n) = Sum_{k=1..n-1} k*A110971(n,k).

1, 3, 8, 21, 52, 126, 296, 685, 1556, 3498, 7768, 17122, 37416, 81308, 175568, 377469, 807604, 1721970, 3657464, 7746838, 16357496, 34459428, 72407728, 151851986, 317777032, 663908196, 1384524656, 2883208740, 5994736336, 12448784824, 25816193952, 53479331357, 110652549620

Offset: 2

Author

N. J. A. Sloane, Sep 20 2009

Keywords

• nonn

Links

• Paolo Xausa, Table of n, a(n) for n = 2..1000
• M. A. Michels and U. Knauer, The congruence classes of paths and cycles, Discr. Math., 309 (2009), 5352-5359. See p. 5356.

Crossrefs

Cf. A110971, A102699.

Main diagonal of A377000.

Programs

Mathematica

A110971[n_] := (n+1)*2^(n-2) - If[OddQ[n], (n-1/2)*Binomial[n-1, (n-1)/2], 2*(n-1)*Binomial[n-2, (n-2)/2]];
Array[A110971, 50, 2] (* Paolo Xausa, Oct 13 2024 *)

Python

from math import comb
def A152086(n): return ((n+1<>1)>>1 if n&1 else (n-1)*comb(n-2,n-2>>1)<<1)) # Chai Wah Wu, Oct 28 2024

Formula

a(n) = A102699(n)/2. - Paolo Xausa, Oct 13 2024, from N. J. A. Sloane formula in A102699.

Extensions

More terms from Paolo Xausa, Oct 13 2024