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 A301976 Number of no-leaf subgraphs of the 3 X n grid. 5
 1, 5, 43, 463, 5193, 58653, 663203, 7500343, 84825873, 959351093, 10849935003, 122709094303, 1387798370393, 15695530423373, 177511143297043, 2007591024144903, 22705175829637153, 256787863292718693, 2904183928335418123, 32845338488555237743 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Also, the number of ways to lay unit-length matchsticks on a 3 X n grid of points in such a way that no end is "orphaned". Conjecture: a(n) mod 10 = 3 for n > 2. LINKS Peter Kagey, Table of n, a(n) for n = 1..949 FORMULA Conjectures from Colin Barker, Mar 30 2018: (Start) G.f.: x*(1 + x)*(1 - 8*x - 3*x^2) / (1 - 12*x + 6*x^2 + 20*x^3 + 5*x^4). a(n) = 12*a(n-1) - 6*a(n-2) - 20*a(n-3) - 5*a(n-4) for n>4. (End) EXAMPLE Three of the a(4) = 463 subgraphs of the 3 X 4 grid with no leaf vertices are +---+ +---+ + + +---+ + + +---+ | | | | | | | | +---+---+ +, + +---+---+, and +---+ +---+. | | | | | | | +---+---+---+ + +---+ + +---+ + + CROSSREFS A093129 is analogous for 2 X (n+1) grids. Sequence in context: A239265 A369023 A274666 * A083070 A191802 A092471 Adjacent sequences: A301973 A301974 A301975 * A301977 A301978 A301979 KEYWORD nonn AUTHOR Peter Kagey, Mar 29 2018 STATUS approved

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Last modified August 4 13:44 EDT 2024. Contains 374923 sequences. (Running on oeis4.)