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 A056116 a(n) = 121*12^(n-2), a(0)=1, a(1)=10. 2
 1, 10, 121, 1452, 17424, 209088, 2509056, 30108672, 361304064, 4335648768, 52027785216, 624333422592, 7492001071104, 89904012853248, 1078848154238976, 12946177850867712, 155354134210412544 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS For n >= 2, a(n) is equal to the number of functions f:{1,2,...,n}->{1,2,3,4,5,6,7,8,9,10,11,12} such that for fixed, different x_1, x_2 in {1,2,...,n} and fixed y_1, y_2 in {1,2,3,4,5,6,7,8,9,10,11,12} we have f(x_1)<>y_1 and f(x_2)<> y_2. - Milan Janjic, Apr 19 2007 a(n) is the number of generalized compositions of n when there are 11*i-1 different types of i, (i=1,2,...). - Milan Janjic, Aug 26 2010 REFERENCES A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196. LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..200 Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets Index entries for linear recurrences with constant coefficients, signature (12). FORMULA a(n) = 12*a(n-1) + (-1)^n*C(2, 2-n). G.f.: (1-x)^2/(1-12*x). a(n) = Sum_{k=0..n} A201780(n,k)*10^k. - Philippe Deléham, Dec 05 2011 E.g.f.: (23 - 12*x + 121*exp(12*x))/144. - G. C. Greubel, Jan 18 2020 MAPLE 1, 10, seq( 121*12^(n-2), n=2..20); # G. C. Greubel, Jan 18 2020 MATHEMATICA LinearRecurrence[{12}, {1, 10, 121}, 20] (* Harvey P. Dale, Oct 20 2015 *) PROG (PARI) concat([1, 10], vector(20, n, 121*12^(n-1) )) \\ G. C. Greubel, Jan 18 2020 (Magma) [1, 10] cat [121*12^(n-2): n in [2..20]]; // G. C. Greubel, Jan 18 2020 (Sage) [1, 10]+[121*12^(n-2) for n in (2..20)] # G. C. Greubel, Jan 18 2020 (GAP) concatenation([1, 10], List([2..20], n-> 121*12^(n-2) )); # G. C. Greubel, Jan 18 2020 CROSSREFS Cf. A055996, A056002. Sequence in context: A202808 A091692 A098309 * A246643 A233084 A081784 Adjacent sequences: A056113 A056114 A056115 * A056117 A056118 A056119 KEYWORD nonn,easy AUTHOR Barry E. Williams, Jul 04 2000 EXTENSIONS More terms from James A. Sellers, Jul 04 2000 STATUS approved

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Last modified August 13 18:32 EDT 2024. Contains 375144 sequences. (Running on oeis4.)