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 A140406 a(n) = binomial(n+6, 6)*8^n. 7
 1, 56, 1792, 43008, 860160, 15138816, 242221056, 3598712832, 50381979648, 671759728640, 8598524526592, 106309030510592, 1275708366127104, 14915974742409216, 170468282770391040, 1909244767028379648 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS With a different offset, number of n-permutations (n >= 6) of 9 objects: p, r, s, t, u, v, z, x, y with repetition allowed, containing exactly six (6) u's. If n=6 then a(0)=1. Example: a(1)=56 because we have uuuuuup, uuuuupu, uuuupuu, uuupuuu, uupuuuu, upuuuuu, puuuuuu, uuuuuur, uuuuuru, uuuuruu, uuuruuu, uuruuuu, uruuuuu, ruuuuuu, uuuuuus, uuuuusu, uuuusuu, uuusuuu, uusuuuu, usuuuuu, suuuuuu, uuuuuut, uuuuutu, uuuutuu, uuutuuu, uutuuuu, utuuuuu, tuuuuuu, uuuuuuv, uuuuuvu, uuuuvuu, uuuvuuu, uuvuuuu, uvuuuuu, vuuuuuu, uuuuuuz, uuuuuzu, uuuuzuu, uuuzuuu, uuzuuuu, uzuuuuu, zuuuuuu, uuuuuux, uuuuuxu, uuuuxuu, uuuxuuu, uuxuuuu, uxuuuuu, xuuuuuu, uuuuuuy, uuuuuyu, uuuuyuu, uuuyuuu, uuyuuuu, uyuuuuu, yuuuuuu. LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..400 Index entries for linear recurrences with constant coefficients, signature (56, -1344, 17920, -143360, 688128, -1835008, 2097152). FORMULA G.f.: 1/(1-8*x)^7. - Zerinvary Lajos, Aug 06 2008 a(n) = 56*a(n-1) - 1344*a(n-2) + 17920*a(n-3) - 143360*a(n-4) + 688128*a(n-5) - 1835008*a(n-6) + 2097152*a(n-7); a(0)=1, a(1)=56, a(2)=1792, a(3)=43008, a(4)=860160, a(5)=15138816, a(6)=242221056. - Harvey P. Dale, Dec 15 2011 MAPLE seq(binomial(n+6, 6)*8^n, n=0..17); MATHEMATICA Table[Binomial[n+6, 6]8^n, {n, 0, 20}] (* or *) LinearRecurrence[ {56, -1344, 17920, -143360, 688128, -1835008, 2097152}, {1, 56, 1792, 43008, 860160, 15138816, 242221056}, 20] (* Harvey P. Dale, Dec 15 2011 *) PROG (MAGMA) [8^n* Binomial(n+6, 6): n in [0..20]]; // Vincenzo Librandi, Oct 16 2011 (PARI) a(n)=binomial(n+6, 6)<<(3*n) \\ Charles R Greathouse IV, Dec 15 2011 CROSSREFS Cf. A000579, A002409, A036220, A036226, A050988, A054337, A140405. Sequence in context: A258465 A050989 A333067 * A075512 A223958 A000504 Adjacent sequences:  A140403 A140404 A140405 * A140407 A140408 A140409 KEYWORD nonn,easy AUTHOR Zerinvary Lajos, Jun 16 2008 STATUS approved

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Last modified January 24 21:49 EST 2022. Contains 350565 sequences. (Running on oeis4.)