A235120 a(n) = b((n+1)/2)^2 if n is odd and a(n) = b(n/2)*b(n/2+1) if n is even, where b = A057452.

64, 152, 361, 1273, 4489, 22177, 109561, 735151, 4932841, 43480517, 383258929, 4299363701, 48229869769, 668098103693, 9254743549921, 154323135646769, 2573343071840641, 50602620151819037, 995057827403377609, 22686465423182125223, 517231963031027272681

Offset: 1

Author

Emeric Deutsch, Jan 18 2014

Keywords

• nonn

Comments

a(n) is the Matula number of the rooted tree obtained by identifying the roots of the trees Q(floor((n+1)/2)) and Q(ceiling((n+1)/2)) defined in A057452.

References

• D. W. Matula, A natural rooted tree enumeration by prime factorization, SIAM Review, 10, 1968, 273.

Links

• E. Deutsch, Tree statistics from Matula numbers, arXiv preprint arXiv:1111.4288, 2011
• E. Deutsch, Rooted tree statistics from Matula numbers, Discrete Appl. Math., 160, 2012, 2314-2322.
• F. Goebel, On a 1-1-correspondence between rooted trees and natural numbers, J. Combin. Theory, B 29 (1980), 141-143.
• I. Gutman and A. Ivic, On Matula numbers, Discrete Math., 150, 1996, 131-142.
• I. Gutman and Yeong-Nan Yeh, Deducing properties of trees from their Matula numbers, Publ. Inst. Math., 53 (67), 1993, 17-22.

Crossrefs

Cf. A057452.

Programs

Maple

b := proc (n) option remember: if n = 1 then 8 else ithprime(b(n-1)) end if: end proc: a := proc (n) if `mod`(n, 2) = 1 then b((1/2)*n+1/2)^2 else b((1/2)*n)*b((1/2)*n+1) end if end proc: seq(a(n), n = 1 .. 17);

Mathematica

b[1] = 8; b[n_] := b[n] = Prime[b[n-1]];
a[n_] := If[OddQ[n], b[(n+1)/2]^2, b[n/2]*b[n/2 + 1]];
Array[a, 21] (* Jean-François Alcover, Nov 26 2017, from Maple *)