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A027949 T(2n,n+1), T given by A027948. 1
1, 4, 25, 97, 309, 894, 2462, 6610, 17519, 46135, 121115, 317484, 831660, 2177872, 5702389, 14929789, 39087537, 102333450, 267913514, 701407870, 1836310955, 4807525939, 12586267895, 32951278872, 86267569944, 225851432284, 591286728337, 1548008754265 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Colin Barker, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (6,-13,13,-6,1).

FORMULA

For n>1, a(n) = Fibonacci(2n+4) - 2n^2 - 3n - 3.

a(1)=1, a(2)=4, a(3)=25, a(4)=97, a(5)=309, a(6)=894, a(n)=6*a(n-1)- 13*a(n-2)+ 13*a(n-3)-6*a(n-4)+a(n-5). - Harvey P. Dale, Apr 20 2012

G.f.: x*(x^5-6*x^4+14*x^3-14*x^2+2*x-1) / ((x-1)^3*(x^2-3*x+1)). - Colin Barker, Nov 19 2014

MATHEMATICA

Join[{1}, Table[Fibonacci[2n+4]-2n^2-3n-3, {n, 2, 40}]] (* or *) Join[ {1}, LinearRecurrence[{6, -13, 13, -6, 1}, {4, 25, 97, 309, 894}, 40]] (* Harvey P. Dale, Apr 20 2012 *)

CoefficientList[Series[(x^5 - 6 x^4 + 14 x^3 - 14 x^2 + 2 x - 1) / ((x - 1)^3 (x^2 - 3 x + 1)), {x, 0, 40}], x] (* Vincenzo Librandi, Nov 20 2014 *)

PROG

(PARI) Vec(x*(x^5-6*x^4+14*x^3-14*x^2+2*x-1)/((x-1)^3*(x^2-3*x+1)) + O(x^100)) \\ Colin Barker, Nov 19 2014

CROSSREFS

Sequence in context: A095669 A323967 A195509 * A226547 A264167 A152215

Adjacent sequences:  A027946 A027947 A027948 * A027950 A027951 A027952

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling

EXTENSIONS

More terms from Harvey P. Dale, Apr 20 2012

STATUS

approved

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Last modified June 16 10:03 EDT 2019. Contains 324152 sequences. (Running on oeis4.)