A027012 a(n) = T(2*n, n+1), T given by A027011.
1, 6, 47, 199, 661, 1954, 5442, 14696, 39065, 103025, 270655, 709716, 1859412, 4869594, 12750611, 33383659, 87401977, 228824086, 599072310, 1568395100, 4106115485, 10749954101, 28143749827, 73681298664, 192900149736, 505019154414, 1322157317687
Offset: 1
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)
Programs
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Mathematica
Join[{1},LinearRecurrence[{6,-13,13,-6,1},{6,47,199,661,1954},30]] (* Harvey P. Dale, Nov 17 2013 *) -
PARI
Vec(x*(1+24*x^2-18*x^3+6*x^4-x^5)/((1-x)^3*(1-3*x+x^2)) + O(x^40)) \\ Colin Barker, Feb 19 2016
Formula
a(1)=1, a(n) = Lucas(2*n+6) - (6*n^2+17*n+18). - Ralf Stephan, May 05 2005
From Colin Barker, Feb 19 2016: (Start)
a(n) = -8 + (2^(-1-n)*((3-sqrt(5))^n*(-15+7*sqrt(5))+(3+sqrt(5))^n*(15+7*sqrt(5))))/sqrt(5) + 13*(1+n) - 6*(1+n)*(2+n) for n>1.
a(n) = 6*a(n-1)-13*a(n-2)+13*a(n-3)-6*a(n-4)+a(n-5) for n>6.
G.f.: x*(1+24*x^2-18*x^3+6*x^4-x^5) / ((1-x)^3*(1-3*x+x^2)).
(End)
Extensions
More terms from Harvey P. Dale, Nov 17 2013