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 A166911 a(n) = (9 + 14*n + 12*n^2 + 4*n^3)/3. 6
 3, 13, 39, 89, 171, 293, 463, 689, 979, 1341, 1783, 2313, 2939, 3669, 4511, 5473, 6563, 7789, 9159, 10681, 12363, 14213, 16239, 18449, 20851, 23453, 26263, 29289, 32539, 36021, 39743, 43713, 47939, 52429, 57191, 62233, 67563, 73189, 79119, 85361, 91923 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS The inverse binomial transform yields the quasi-finite sequence 3,10,16,8,0,.. (0 continued). These are the bottom-left numbers in the blocks (each with 2 rows) shown in A172002, the atomic number of the leftmost element in the 2nd, 4th, 6th etc. row of the Janet table. REFERENCES Charles Janet, La structure du noyau de l'atome .., Nov 1927, page 15. LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..10000 Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1). FORMULA First differences: a(n)-a(n-1) = 2+4*n+4*n^2 = 1+(1+2n)^2 = 1 + A016754(n+1) = A069894(n+1). Second differences: a(n) - 2*a(n-1) + a(n-2) = 8*n = A008590(n+2). Third differences: a(n) - 3*a(n-1) + 3*a(n-2) - a(n-3) = 8. a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). G.f.: (3 + x + 5*x^2 - x^3)/(1-x)^4. a(n) = A166464(n) + 2*(n+1)^2 = A166464(n) + A001105(n+1). E.g.f.: (1/3)*(9 + 30*x + 24*x^2 + 4*x^3)*exp(x). - G. C. Greubel, May 28 2016 MATHEMATICA LinearRecurrence[{4, -6, 4, -1}, {3, 13, 39, 89}, 100] (* G. C. Greubel, May 28 2016 *) PROG (Magma) [(9+14*n+12*n^2+4*n^3)/3: n in [0..40] ]; // Vincenzo Librandi, Aug 06 2011 (PARI) a(n)=n*(4*n^2+12*n+14)/3+3 \\ Charles R Greathouse IV, Dec 21 2011 CROSSREFS Sequence in context: A072790 A323009 A328703 * A103657 A320661 A122504 Adjacent sequences: A166908 A166909 A166910 * A166912 A166913 A166914 KEYWORD nonn,easy AUTHOR Paul Curtz, Oct 23 2009 EXTENSIONS Edited and extended by R. J. Mathar, Mar 02 2010 STATUS approved

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Last modified January 29 00:02 EST 2023. Contains 359905 sequences. (Running on oeis4.)