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 A131253 Row sums of triangle A131252. 3
 1, 3, 8, 17, 34, 64, 117, 209, 368, 641, 1108, 1904, 3257, 5551, 9432, 15985, 27030, 45616, 76845, 129245, 217056, 364033, 609768, 1020192, 1705009, 2846619, 4748072, 7912529, 13174858, 21919456, 36440613, 60538409, 100503632, 166744961, 276476092, 458151440 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Andrew Howroyd, Table of n, a(n) for n = 0..500 Index entries for linear recurrences with constant coefficients, signature (4, -4, -2, 4, 0, -1) FORMULA From Andrew Howroyd, Aug 09 2018: (Start) a(n) = Sum_{k=0..n} (k+1)*(Sum_{i=0..k} binomial(n-k, k-i)). a(n) = 4*a(n-1) - 4*a(n-2) - 2*a(n-3) + 4*a(n-4) - a(n-6). G.f.: (1 - x - x^3)/((1 - x)^2*(1 - x - x^2)^2). (End) EXAMPLE a(3) = 17 = sum of row 3 terms of A131252: (7 + 6 + 3 + 1). MATHEMATICA LinearRecurrence[{4, -4, -2, 4, 0, -1}, {1, 3, 8, 17, 34, 64}, 40] (* Vincenzo Librandi, Aug 10 2018 *) PROG (PARI) Vec((1 - x - x^3)/((1 - x)^2*(1 - x - x^2)^2) + O(x^40)) \\ Andrew Howroyd, Aug 09 2018 (PARI) a(n)={sum(k=0, n, (k+1)*sum(i=0, k, binomial(n-k, k-i)))} \\ Andrew Howroyd, Aug 09 2018 (MAGMA) I:=[1, 3, 8, 17, 34, 64]; [n le 6 select I[n] else 4*Self(n-1)- 4*Self(n-2)-2*Self(n-3)+4*Self(n-4)-Self(n-6): n in [1..40]]; // Vincenzo Librandi, Aug 10 2018 CROSSREFS Row sums of A131252. Sequence in context: A029859 A305105 A163312 * A145071 A182734 A327608 Adjacent sequences:  A131250 A131251 A131252 * A131254 A131255 A131256 KEYWORD nonn AUTHOR Gary W. Adamson, Jun 23 2007 EXTENSIONS Terms a(10) and beyond from Andrew Howroyd, Aug 09 2018 STATUS approved

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Last modified May 16 12:24 EDT 2021. Contains 343943 sequences. (Running on oeis4.)