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 A077843 Expansion of (1-x)/(1-2*x-2*x^2-2*x^3). 1
 1, 1, 4, 12, 34, 100, 292, 852, 2488, 7264, 21208, 61920, 180784, 527824, 1541056, 4499328, 13136416, 38353600, 111978688, 326937408, 954539392, 2786910976, 8136775552, 23756451840, 69360276736, 202507008256, 591247473664, 1726229517312, 5039967998464 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Invert transform of the sequence 1,3,5,5,5,5,... which has g.f. (1+2x+2x^2)/(1-x). - Paul Barry, Mar 01 2011 LINKS Index entries for linear recurrences with constant coefficients, signature (2,2,2). FORMULA a(n) = sum(k=1..n, sum(i=k..n,(sum(j=0..k, binomial(j,-3*k+2*j+i)*2^(-2*k+j+i)* binomial(k,j)))*binomial(n+k-i-1,k-1))). - Vladimir Kruchinin, May 05 2011 EXAMPLE Eigensequence of the triangle   1,   3, 1,   5, 3, 1,   5, 5, 3, 1,   5, 5, 5, 3, 1,   5, 5, 5, 5, 3, 1,   5, 5, 5, 5, 5, 3, 1,   5, 5, 5, 5, 5, 5, 3, 1,   ... - Paul Barry, Mar 01 2011 PROG (Sage) from sage.combinat.sloane_functions import recur_gen3 it = recur_gen3(0, 1, 1, 2, 2, 2) [it.next() for i in range(35)] # Zerinvary Lajos, Jun 25 2008 (Maxima) a(n):=sum(sum((sum(binomial(j, -3*k+2*j+i)*2^(-2*k+j+i)*binomial(k, j), j, 0, k))*binomial(n+k-i-1, k-1), i, k, n), k, 1, n); /* Vladimir Kruchinin, May 05 2011 */ (PARI) Vec((1-x)/(1-2*x-2*x^2-2*x^3)+O(x^99)) \\ Charles R Greathouse IV, Sep 27 2012 CROSSREFS Sequence in context: A005056 A014143 A077994 * A061703 A126948 A131593 Adjacent sequences:  A077840 A077841 A077842 * A077844 A077845 A077846 KEYWORD nonn,easy AUTHOR N. J. A. Sloane, Nov 17 2002 STATUS approved

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Last modified October 18 18:56 EDT 2019. Contains 328197 sequences. (Running on oeis4.)