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 A355227 Irregular triangle read by rows where T(n,k) is the number of independent sets of size k in the n-folded cube graph. 1
 1, 2, 1, 4, 1, 8, 12, 8, 2, 1, 16, 80, 160, 120, 16, 1, 32, 400, 2560, 9280, 20256, 28960, 31520, 29880, 24320, 16336, 8768, 3640, 1120, 240, 32, 2, 1, 64, 1792, 29120, 307440, 2239552, 11682944, 44769920, 128380880, 279211520, 464621248, 593908224, 582529360, 435648640, 245610720, 102886976, 31658620, 7189056, 1239840, 165760, 17584, 1408, 64 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,2 COMMENTS The independence number alpha(G) of a graph is the cardinality of the largest independent vertex set. The n-folded cube has alpha(G) = A058622(n-1). The independence polynomial for the n-folded cube is given by Sum_{k=0..alpha(G)} T(n,k)*t^k. Since 0 <= k <= alpha(G), row n has length A058622(n-1) + 1. LINKS Table of n, a(n) for n=2..56. Eric Weisstein's World of Mathematics, Independence polynomial Eric Weisstein's World of Mathematics, Folded cube graph EXAMPLE Triangle begins: k = 1 2 3 4 5 6 n = 2: 1, 2 n = 3: 1, 4 n = 4: 1, 8, 12, 8, 2 n = 5: 1, 16, 80, 160, 120, 16 The 5-folded cube graph has independence polynomial 1 + 16*t + 80*t^2 + 160*t^3 + 120*t^4 + 16*t^5. PROG (Sage) from sage.graphs.independent_sets import IndependentSets def row(n): g = graphs.FoldedCubeGraph(n) if n % 2 == 0: setCounts = [0] * (pow(2, n-2) + 1) else: size = int(pow(2, n-2) - 1/4 * (1-pow(-1, n)) * math.comb(n-1, 1/2 * (n-1)) + 1) setCounts = [0] * size for Iset in IndependentSets(g): setCounts[len(Iset)] += 1 return setCounts CROSSREFS Cf. A058622. Sequence in context: A107061 A112481 A134851 * A264148 A038001 A147080 Adjacent sequences: A355224 A355225 A355226 * A355228 A355229 A355230 KEYWORD nonn,tabf AUTHOR Christopher Flippen, Jun 24 2022 STATUS approved

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Last modified June 8 23:10 EDT 2023. Contains 363165 sequences. (Running on oeis4.)