login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A342939 a(n) is the Skolem number of the triangular grid graph T_n. 2
1, 2, 5, 7, 11, 16, 22, 29, 37, 46, 56, 67, 79, 92, 106, 121, 137, 154, 172, 191, 211, 232, 254, 277, 301, 326, 352, 379, 407, 436, 466, 497, 529, 562, 596, 631, 667, 704, 742, 781, 821, 862, 904, 947, 991, 1036, 1082, 1129, 1177, 1226, 1276, 1327, 1379, 1432, 1486 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
For the meaning of Skolem number of a graph, see Definitions 1.4 and 1.5 in Carrigan and Green.
LINKS
Braxton Carrigan and Garrett Green, Skolem Number of Subgraphs on the Triangular Lattice, Communications on Number Theory and Combinatorial Theory 2 (2021), Article 2.
FORMULA
O.g.f.: x*(1 - x + 2*x^2 - 3*x^3 + 3*x^4 - x^5)/(1 - x)^3.
E.g.f.: exp(x)*(2 + x^2)/2 - 1 + x^3/6.
a(n) = 3*a(n-1) - 3*a(n-2) - a(n-3) for n > 6.
Except for a(3) = 5:
a(n) = 1 + n*(n - 1)/2 (see Theorem 2.5 in Carrigan and Green).
a(n) = 1 + A161680(n).
a(n) = A152947(n-1).
MATHEMATICA
LinearRecurrence[{3, -3, 1}, {1, 2, 5, 7, 11, 16}, 55]
CROSSREFS
For n > 1, 3*A002061(n) gives the Skolem number of the hexagonal grid graph H_n.
Sequence in context: A317242 A217302 A062409 * A089781 A144832 A309290
KEYWORD
nonn,easy
AUTHOR
Stefano Spezia, Mar 30 2021
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 25 09:18 EDT 2024. Contains 371967 sequences. (Running on oeis4.)