login
A027954
a(n) = T(2n+1, n+2), T given by A027948.
1
1, 5, 41, 189, 674, 2098, 6050, 16703, 44995, 119575, 315460, 829060, 2174596, 5698329, 14924829, 39081553, 102326310, 267905078, 701397990, 1836299475, 4807512695, 12586252715, 32951261576, 86267550344, 225851410184, 591286703533, 1548008726545, 4052739505253, 10610209821610
OFFSET
1,2
FORMULA
G.f.: x*(1 -2*x +25*x^2 -29*x^3 +19*x^4 -7*x^5 +x^6)/((1-x)^4*(1 -3*x +x^2)). - Colin Barker, Nov 25 2014
From G. C. Greubel, Sep 30 2019: (Start)
a(n) = Sum_{j=0..n-1} binomial(2*n-j+1, j+4) for n >= 2.
a(n) = Fibonacci(2*n+6) - (24 + 23*n + 12*n^2 + 4*n^3)/3 for n >= 2. (End)
MAPLE
with(combinat); seq(`if`(n=1, 1, fibonacci(2*n+6) -(24 +23*n +12*n^2 +4*n^3)/3), n=1..40); # G. C. Greubel, Sep 30 2019
MATHEMATICA
Table[If[n==1, 1, Fibonacci[2*n+6] - (24 +23*n +12*n^2 +4*n^3)/3], {n, 1, 40}] (* G. C. Greubel, Sep 30 2019 *)
PROG
(PARI) vector(40, n, if(n==1, 1, fibonacci(2*n+6) -(24 +23*n +12*n^2 + 4*n^3)/3 )) \\ G. C. Greubel, Sep 30 2019
(Magma) [1] cat [Fibonacci(2*n+6) -(24 + 23*n + 12*n^2 + 4*n^3)/3: n in [2..40]]; // G. C. Greubel, Sep 30 2019
(Sage) [1]+[fibonacci(2*n+6) -(24 + 23*n + 12*n^2 + 4*n^3)/3 for n in (2..40)] # G. C. Greubel, Sep 30 2019
(GAP) Concatenation([1], List([2..40], n-> Fibonacci(2*n+6) -(24 + 23*n + 12*n^2 + 4*n^3)/3 )); # G. C. Greubel, Sep 30 2019
CROSSREFS
Sequence in context: A271001 A258229 A096946 * A270623 A322420 A270165
KEYWORD
nonn
EXTENSIONS
Name corrected and terms a(22) onward by G. C. Greubel, Sep 30 2019
STATUS
approved