A354763 a(n) is the minimum number of square tiles needed for constructing a figure whose corresponding graph has n cycles.

0, 4, 7, 6, 9, 12, 8, 11, 14, 13, 10, 13, 16, 15, 18, 12, 15, 18, 17, 20, 23, 14, 17, 20, 19, 22, 25, 21, 16, 19, 22, 21, 24, 27, 23, 26, 18, 21, 24, 23, 26, 29, 25, 28, 31, 20, 23, 26, 25, 28, 31, 27, 30, 33, 32, 22, 25, 28, 27, 30, 33, 29, 32, 35, 34, 31, 24

Offset

0,2

Comments

The square tiles are connected only at corners.

Links

Table of n, a(n) for n=0..66.

Stefano Spezia, Illustrations for n = 1..10

Formula

a(n) = 1 + Sum_{i=1..A057945(n)} sqrt(1 + 8*A354762(n, i)) for n > 0.

a(A000217(n)) = A163300(n+1).

Mathematica

r[n_]:=First[IntegerPartitions[n, All, Table[k(k+1)/2, {k, Sqrt[1+8n]}]]]; (* A354762 *)
Join[{0}, Table[1+Sum[Sqrt[1+8Part[r[n], i]], {i, Length[r[n]]}], {n, 66}]]

Crossrefs

Cf. A000217, A057945, A163300, A354762.

Sequence in context: A293904 A069286 A079354 * A255248 A122460 A256659

Adjacent sequences: A354760 A354761 A354762 * A354764 A354765 A354766

Keyword

nonn,easy

Author

Stefano Spezia, Jun 06 2022

Status

approved