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 A291444 Number of symmetric maximal irredundant sets in the n-path graph. 2
 1, 0, 2, 2, 2, 2, 3, 3, 5, 6, 7, 6, 10, 12, 15, 15, 22, 23, 33, 35, 48, 48, 71, 75, 103, 106, 152, 158, 225, 234, 329, 338, 484, 505, 710, 734, 1044, 1084, 1536, 1594, 2257, 2335, 3317, 3444, 4871, 5047, 7161, 7429, 10528, 10916, 15470, 16033, 22737, 23582 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 LINKS Andrew Howroyd, Table of n, a(n) for n = 1..200 Eric Weisstein's World of Mathematics, Maximal Irredundant Set Eric Weisstein's World of Mathematics, Path Graph Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, -1, 0, -2, 0, -1, 0, 2, 0, 1, 0, 0, 0, 0, 0, -1). FORMULA a(n) = a(n-4) + a(n-6) + a(n-8) + a(n-10) - a(n-14) - 2*a(n-16) - a(n-18) + 2*a(n-20) + a(n-22) - a(n-28) for n > 28. G.f.: x*(1 + 2*x^2 + 2*x^3 + x^4 + 2*x^5 + x^7 + 2*x^9 - x^10 - x^11 - 2*x^12 - x^13 - x^14 - 2*x^15 + x^16 - 2*x^17 + 3*x^18 + 2*x^19 + x^20 + x^21 - x^22 - x^24 - x^26 - x^27)/(1 - x^4 - x^6 - x^8 - x^10 + x^14 + 2*x^16 + x^18 - 2*x^20 - x^22 + x^28). EXAMPLE Case n=5: maximal irredundant sets represented as binary words are {00110, 01001, 01010, 01100, 10010, 10101}. Of these, only 01010 and 10101 are symmetrical, so a(5) = 2. PROG (PARI) Vec((1 + 2*x^2 + 2*x^3 + x^4 + 2*x^5 + x^7 + 2*x^9 - x^10 - x^11 - 2*x^12 - x^13 - x^14 - 2*x^15 + x^16 - 2*x^17 + 3*x^18 + 2*x^19 + x^20 + x^21 - x^22 - x^24 - x^26 - x^27)/(1 - x^4 - x^6 - x^8 - x^10 + x^14 + 2*x^16 + x^18 - 2*x^20 - x^22 + x^28) + O(x^50)) CROSSREFS Cf. A291055. Sequence in context: A005858 A285798 A321346 * A219795 A082602 A216644 Adjacent sequences:  A291441 A291442 A291443 * A291445 A291446 A291447 KEYWORD nonn AUTHOR Andrew Howroyd, Aug 23 2017 STATUS approved

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Last modified May 13 17:46 EDT 2021. Contains 343864 sequences. (Running on oeis4.)