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A360201
Number of induced paths in the n-ladder graph P_2 X P_n.
2
1, 8, 25, 58, 117, 218, 387, 666, 1123, 1868, 3079, 5044, 8229, 13388, 21741, 35262, 57145, 92558, 149863, 242590, 392631, 635408, 1028235, 1663848, 2692297, 4356368, 7048897, 11405506, 18454653, 29860418, 48315339, 78176034, 126491659, 204667988
OFFSET
1,2
LINKS
Eric Weisstein's World of Mathematics, Ladder Graph
FORMULA
a(n) = 3*a(n-1) - 2*a(n-2) - a(n-3) + a(n-4) for n > 4.
G.f.: x*(1 + 5*x + 3*x^2)/((1 - x)^2*(1 - x - x^2)).
MATHEMATICA
LinearRecurrence[{3, -2, -1, 1}, {1, 8, 25, 58}, 40] (* Harvey P. Dale, Dec 28 2023 *)
PROG
(PARI) Vec((1 + 5*x + 3*x^2)/((1 - x)^2*(1 - x - x^2)) + O(x^40))
CROSSREFS
Row 2 of A360199.
Sequence in context: A143371 A131423 A270867 * A004640 A250321 A011924
KEYWORD
nonn,easy
AUTHOR
Andrew Howroyd, Jan 29 2023
STATUS
approved