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 A365607 Number of degree 3 vertices in the n-Sierpinski carpet graph. 8
 0, 40, 328, 2536, 19912, 158056, 1260616, 10073320, 80551624, 644308072, 5154149704, 41232252904, 329855188936, 2638833008488, 21110638558792, 168885031942888, 1351080025960648, 10808639518937704, 86469114085259080, 691752906483344872, 5534023233270575560, 44272185810376054120 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The level 0 Sierpinski carpet graph is a single vertex. The level n Sierpinski carpet graph is formed from 8 copies of level n-1 by joining boundary vertices between adjacent copies. LINKS Paolo Xausa, Table of n, a(n) for n = 1..1000 Allan Bickle, Degrees of Menger and Sierpinski Graphs, Congr. Num. 227 (2016) 197-208. Allan Bickle, MegaMenger Graphs, The College Mathematics Journal, 49 1 (2018) 20-26. Eric Weisstein's World of Mathematics, Sierpiński Carpet Graph Index entries for linear recurrences with constant coefficients, signature (12,-35,24). FORMULA a(n) = (3/5)*8^n + (16/15)*3^n - 8. a(n) = 8*a(n-1) - 16*3^(n-2) + 56. a(n) = 8^n - A365606(n) - A365608(n). 3*a(n) = 2*A271939(n) - 2*A365606(n) - 4*A365608(n). G.f.: 8*x^2*(5 - 19*x)/((1 - x)*(1 - 3*x)*(1 - 8*x)). - Stefano Spezia, Sep 12 2023 EXAMPLE The level 1 Sierpinski carpet graph is an 8-cycle, which has 8 degree 2 vertices and 0 degree 3 or 4 vertices. Thus a(1) = 0. MATHEMATICA LinearRecurrence[{12, -35, 24}, {0, 40, 328}, 30] (* Paolo Xausa, Oct 16 2023 *) PROG (Python) def A365607(n): return ((3<<3*n)+(3**(n-1)<<4))//5-8 # Chai Wah Wu, Nov 27 2023 CROSSREFS Cf. A001018 (order), A271939 (size). Cf. A365606 (degree 2), A365607 (degree 3), A365608 (degree 4). Cf. A009964, A291066, A359452, A359453, A291066, A083233, A332705 (Menger sponge graph). Sequence in context: A061993 A087954 A160328 * A247407 A251431 A285919 Adjacent sequences: A365604 A365605 A365606 * A365608 A365609 A365610 KEYWORD nonn,easy AUTHOR Allan Bickle, Sep 12 2023 STATUS approved

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Last modified March 4 05:23 EST 2024. Contains 370522 sequences. (Running on oeis4.)