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 A123350 a(n) = (n^4 + 2n^3 + 5n^2 + 4)/4. 2
 1, 3, 14, 46, 117, 251, 478, 834, 1361, 2107, 3126, 4478, 6229, 8451, 11222, 14626, 18753, 23699, 29566, 36462, 44501, 53803, 64494, 76706, 90577, 106251, 123878, 143614, 165621, 190067, 217126, 246978, 279809, 315811, 355182, 398126, 444853 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Kekulé numbers for certain benzenoids. - Emeric Deutsch, Oct 16 2006 Form the 2 X 3 matrix with first row C(n,0), C(n,1), and C(n,2) and second row C(n+1,0), C(n+1,1), and C(n+1,2), multiply it by its transpose to get a 2 X 2 matrix: its determinant = a(n). - J. M. Bergot, Sep 05 2013 REFERENCES S. J. Cyvin and I. Gutman, Kekulé structures in benzenoid hydrocarbons, Lecture Notes in Chemistry, No. 46, Springer, New York, 1988 (see p. 120). LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1). FORMULA G.f.: (-1 + 2*x - 9*x^2 + 4*x^3 - 2*x^4) / (x-1)^5 . - R. J. Mathar, Oct 19 2012 a(n) = 1 + A117717(n+1). - R. J. Mathar, Sep 15 2013 E.g.f.: (x^4 + 8*x^3 + 18*x^2 + 8*x + 4)*exp(x)/4. - G. C. Greubel, Oct 12 2017 MAPLE a:=n->(n^4+2*n^3+5*n^2+4)/4: seq(a(n), n=0..40); # Emeric Deutsch, Oct 16 2006 MATHEMATICA Table[(n^4 + 2*n^3 + 5*n^2 + 4)/4, {n, 0, 50}] (* G. C. Greubel, Oct 12 2017 *) PROG (PARI) for(n=0, 50, print1((n^4 + 2*n^3 + 5*n^2 + 4)/4, ", ")) \\ G. C. Greubel, Oct 12 2017 (MAGMA) [(n^4 + 2*n^3 + 5*n^2 + 4)/4: n in [0..30]]; // G. C. Greubel, Oct 12 2017 CROSSREFS Sequence in context: A032150 A032055 A180785 * A027953 A264501 A104196 Adjacent sequences:  A123347 A123348 A123349 * A123351 A123352 A123353 KEYWORD nonn,easy AUTHOR N. J. A. Sloane, Oct 10 2006 EXTENSIONS More terms from Emeric Deutsch, Oct 16 2006 STATUS approved

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Last modified August 11 12:12 EDT 2022. Contains 356065 sequences. (Running on oeis4.)