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 A238275 a(n) = (4*7^n - 1)/3. 5
 1, 9, 65, 457, 3201, 22409, 156865, 1098057, 7686401, 53804809, 376633665, 2636435657, 18455049601, 129185347209, 904297430465, 6330082013257, 44310574092801, 310174018649609, 2171218130547265, 15198526913830857, 106389688396816001, 744727818777712009 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Sum of n-th row of triangle of powers of 7: 1; 1 7 1; 1 7 49 7 1; 1 7 49 343 49 7 1; ... Number of cubes in the crystal structure cubic carbon CCC(n+1), defined in the Baig et al. and in the Gao et al. references. - Emeric Deutsch, May 28 2018 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..200 A. Q. Baig, M. Imran, W. Khalid, and M. Naeem, Molecular description of carbon graphite and crystal cubic carbon structures, Canadian J. Chem., 95, 674-686, 2017. W. Gao, M. K. Siddiqui, M. Naeem and N. A. Rehman, Topological characterization of carbon graphite and crystal cubic carbon structures, Molecules, 22, 1496, 1-12, 2017. FORMULA G.f.: (1+x)/((1-x)*(1-7*x)). a(n) = 7*a(n-1) + 2, a(0) = 1. a(n) = 8*a(n-1) - 7*a(n-2), a(0) = 1, a(1) = 9. a(n) = Sum_{k=0..n} A112468(n,k)*8^k. EXAMPLE a(0) = 1; a(1) = 1 + 7 + 1 = 9; a(2) = 1 + 7 + 49 + 7 + 1 = 65; a(3) = 1 + 7 + 49 + 343 + 49 + 7 + 1 = 457; etc. MATHEMATICA Table[(4 7^n - 1)/3, {n, 0, 40}] (* Vincenzo Librandi, Feb 23 2014 *) PROG (MAGMA) [(4*7^n - 1)/3: n in [0..30]]; // Vincenzo Librandi, Feb 23 2014 CROSSREFS Cf. Similar sequences: A151575, A000012, A040000, A005408, A033484, A048473, A020989, A057651, A061801, this sequence, A238276, A138894, A090843, A199023. Cf. A112468, A112739. Sequence in context: A102902 A127534 A037548 * A287816 A036731 A020234 Adjacent sequences:  A238272 A238273 A238274 * A238276 A238277 A238278 KEYWORD nonn,easy AUTHOR Philippe Deléham, Feb 21 2014 STATUS approved

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Last modified May 7 20:36 EDT 2021. Contains 343652 sequences. (Running on oeis4.)