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 A002783 2*(3^n - 2^n) + 1. (Formerly M2892 N1159) 7
 1, 3, 11, 39, 131, 423, 1331, 4119, 12611, 38343, 116051, 350199, 1054691, 3172263, 9533171, 28632279, 85962371, 258018183, 774316691, 2323474359, 6971471651, 20916512103, 62753730611, 188269580439, 564825518531, 1694510110023, 5083597438931, 15250926534519 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Binomial transform of A095121. - R. J. Mathar, Oct 05 2012 Create a triangle having its left and right border both equal to the n-th row of Pascal's triangle, and internal terms m(i,j)=m(i-1,j-1)+m(i-1,j). Then the sum of all elements equals a(n). - J. M. Bergot, Oct 07 2012, edited by M. F. Hasler, Oct 10 2012 First differences of A090326 (with offset 1). - Wesley Ivan Hurt, Jul 08 2014 REFERENCES H. Gupta, On a problem in parity, Indian J. Math., 11 (1969), 157-163. N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence). N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 H. Gupta, On a problem in parity, Indian J. Math., 11 (1969), 157-163. [Annotated scanned copy] Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009. Simon Plouffe, 1031 Generating Functions, Appendix to Thesis, Montreal, 1992 Index entries for linear recurrences with constant coefficients, signature (6,-11,6). FORMULA G.f.: ( -1+3*x-4*x^2 ) / ( (x-1)*(3*x-1)*(2*x-1) ). - Simon Plouffe in his 1992 dissertation. a(n+1) - a(n) = 2*A027649(n). - R. J. Mathar, Oct 05 2012 EXAMPLE For n=3, one has the triangle with left and right border (1,3,3,1): 1 3 3 3 6 3 1 9 9 1, and sum of all elements equal to 39 = a(3). - J. M. Bergot and M. F. Hasler, Oct 10 2012 MAPLE A002783:=n->2*(3^n - 2^n)+1: seq(A002783(n), n=0..30); # Wesley Ivan Hurt, Jul 08 2014 MATHEMATICA CoefficientList[Series[(-1 + 3*x - 4*x^2)/((x - 1)*(3*x - 1)*(2*x - 1)), {x, 0, 30}], x] (* Wesley Ivan Hurt, Jul 08 2014 *) PROG (Magma) [2*(3^n - 2^n)+1 : n in [0..30]]; // Wesley Ivan Hurt, Jul 08 2014 (PARI) a(n)=2*(3^n-2^n)+1 \\ Charles R Greathouse IV, Oct 07 2015 CROSSREFS Cf. A027649, A090326, A095121. Sequence in context: A089579 A227638 A166336 * A289834 A007482 A134760 Adjacent sequences: A002780 A002781 A002782 * A002784 A002785 A002786 KEYWORD nonn,easy AUTHOR N. J. A. Sloane. EXTENSIONS More terms from Wesley Ivan Hurt, Jul 08 2014 STATUS approved

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Last modified September 27 20:41 EDT 2023. Contains 365714 sequences. (Running on oeis4.)