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 A124820 Expansion of (1-x)/(1-4*x+3*x^2-x^3). 6
 1, 3, 9, 28, 88, 277, 872, 2745, 8641, 27201, 85626, 269542, 848491, 2670964, 8407925, 26467299, 83316385, 262271568, 825604416, 2598919345, 8181135700, 25753389181, 81069068969, 255197244033, 803335158406, 2528817970494 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Row sums of A124819. Let M = a triangle with the triangular series in every column, but the leftmost column is shifted upwards one row. Then A124820 = Lim_{n->inf} M^n, the left-shifted vector considered as a sequence. - Gary W. Adamson, Jul 27 2010 Second trisection of Narayana's cows sequence A000930. - Oboifeng Dira, Aug 03 2016 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (4,-3,1). FORMULA a(n) = sum( k=0..n, C(n+2k+1, 3k+1) ). a(n) = A052529(n+1) - A052529(n), n>1. - R. J. Mathar, Dec 15 2008 MATHEMATICA CoefficientList[Series[(1 - x)/(1 - 4 x + 3 x^2 - x^3), {x, 0, 30}], x] (* Wesley Ivan Hurt, Jun 20 2014 *) LinearRecurrence[{4, -3, 1}, {1, 3, 9}, 30] (* Harvey P. Dale, Apr 29 2016 *) Table[Sum[Binomial[n + 2 k + 1, 3 k + 1], {k, 0, n}], {n, 0, 25}] (* Michael De Vlieger, Aug 03 2016 *) PROG (PARI) a(n)=([0, 1, 0; 0, 0, 1; 1, -3, 4]^n*[1; 3; 9])[1, 1] \\ Charles R Greathouse IV, Aug 03 2016 CROSSREFS Sequence in context: A339064 A118365 A095716 * A022020 A195675 A170953 Adjacent sequences:  A124817 A124818 A124819 * A124821 A124822 A124823 KEYWORD nonn,easy AUTHOR Paul Barry, Nov 08 2006 STATUS approved

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Last modified August 5 15:41 EDT 2021. Contains 346477 sequences. (Running on oeis4.)