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 A027950 a(n) = T(2n,n+2), T given by A027948. 1
 1, 6, 63, 344, 1383, 4685, 14323, 41119, 113590, 306605, 816410, 2157046, 5674578, 14893364, 39040633, 102273950, 267839033, 701315739, 1836198205, 4807389285, 12586103720, 32951083211, 86267338468, 225851160284, 591286410708, 1548008385490 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,2 LINKS Colin Barker, Table of n, a(n) for n = 2..1000 Index entries for linear recurrences with constant coefficients, signature (8,-26,45,-45,26,-8,1). FORMULA G.f.: x^2*(1-2*x+41*x^2-49*x^3+44*x^4-26*x^5+8*x^6-x^7)/((1-3*x+x^2)*(1-x)^5). - Ralf Stephan, Apr 24 2004 From G. C. Greubel, Sep 29 2019: (Start) a(n) = Sum_{j=0..n-2} binomial(2*n-j, j+5), with a(2) = 1 for n >= 2. a(n) = Fibonacci(2*n+6) - (48 + 47*n + 23*n^2 + 4*n^3 + 4*n^4)/6 for n >= 3. (End) MAPLE with(combinat); seq(`if`(n=2, 1, fibonacci(2*n+6) -(48 +47*n +23*n^2 +4*n^3 +4*n^4)/6), n=2..40); # G. C. Greubel, Sep 29 2019 MATHEMATICA Table[If[n==2, 1, Fibonacci[2*n+6] -(48 +47*n +23*n^2 +4*n^3 +4*n^4)/6], {n, 2, 40}] (* G. C. Greubel, Sep 29 2019 *) CoefficientList[Series[x^2(1-2x+41x^2-49x^3+44x^4-26x^5+8x^6-x^7)/ ((1-3x+x^2)(1-x)^5), {x, 0, 30}], x] (* or *) LinearRecurrence[{8, -26, 45, -45, 26, -8, 1}, {1, 6, 63, 344, 1383, 4685, 14323, 41119}, 30] (* Harvey P. Dale, Aug 15 2021 *) PROG (PARI) Vec(x^2*(x^7-8*x^6+26*x^5-44*x^4+49*x^3-41*x^2+2*x-1)/((x-1)^5* (x^2-3*x+1)) + O(x^40)) \\ Colin Barker, Nov 19 2014 (PARI) vector(40, n, my(m=n+1); if(m==2, 1, fibonacci(2*m+6) -(48 +47*m +23*m^2 +4*m^3 +4*m^4)/6) ) \\ G. C. Greubel, Sep 29 2019 (Magma) [1] cat [Fibonacci(2*n+6) -(48 +47*n +23*n^2 +4*n^3 +4*n^4)/6: n in [3..40]]; // G. C. Greubel, Sep 29 2019 (Sage) [1]+[fibonacci(2*n+6) -(48 +47*n +23*n^2 +4*n^3 +4*n^4)/6 for n in (3..40)] # G. C. Greubel, Sep 29 2019 (GAP) Concatenation([1], List([3..40], n-> Fibonacci(2*n+6) -(48 +47*n +23*n^2 +4*n^3 +4*n^4)/6) ); # G. C. Greubel, Sep 29 2019 CROSSREFS Bisection of A053739. Cf. A000045, A027948. Sequence in context: A339239 A055005 A027811 * A184447 A053700 A296393 Adjacent sequences: A027947 A027948 A027949 * A027951 A027952 A027953 KEYWORD nonn,easy AUTHOR Clark Kimberling EXTENSIONS More terms from Colin Barker, Nov 19 2014 STATUS approved

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Last modified November 28 18:34 EST 2023. Contains 367419 sequences. (Running on oeis4.)