A027952 a(n) = T(2n,n+4), T given by A027948.
1, 10, 231, 2300, 14820, 72905, 298925, 1077748, 3540913, 10871723, 31775031, 89633545, 246575109, 666605513, 1781049298, 4721874921, 12456394685, 32758238316, 85985810716, 225446971141, 590714939822, 1547211717890, 4051642877482, 10608719012366, 27775885869046
Offset: 4
Keywords
Links
- G. C. Greubel, Table of n, a(n) for n = 4..1000
- Index entries for linear recurrences with constant coefficients, signature (12,-64,201,-414,588,-588,414,-201,64,-12,1).
Programs
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GAP
Concatenation([1], List([5..40], n-> Fibonacci(2*n+10) -(138600 +133530*n +63999*n^2 + 20286*n^3 +5929*n^4 +616*n^6 -96*n^7 +16*n^8)/2520) ); # G. C. Greubel, Sep 29 2019
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Magma
[1] cat [Fibonacci(2*n+10) -(138600 +133530*n +63999*n^2 + 20286*n^3 +5929*n^4 +616*n^6 -96*n^7 +16*n^8)/2520: n in [5..40]]; // G. C. Greubel, Sep 29 2019
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Maple
with(combinat); seq(`if`(n=4,1, fibonacci(2*n+10) -(138600 +133530*n +63999*n^2 + 20286*n^3 +5929*n^4 +616*n^6 -96*n^7 +16*n^8)/2520), n=4..40); # G. C. Greubel, Sep 29 2019
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Mathematica
Table[If[n==4, 1, Fibonacci[2*n+10] - (138600 +133530*n +63999*n^2 + 20286*n^3 +5929*n^4 +616*n^6 -96*n^7 +16*n^8)/2520], {n, 4, 40}] (* G. C. Greubel, Sep 29 2019 *) -
PARI
vector(40, n, my(m=n+3); if(m==4, 1, fibonacci(2*m+10) -(138600 +133530*m +63999*m^2 + 20286*m^3 +5929*m^4 +616*m^6 -96*m^7 +16*m^8)/2520) ) \\ G. C. Greubel, Sep 29 2019
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Sage
[1]+[fibonacci(2*n+10) -(138600 +133530*n +63999*n^2 + 20286*n^3 +5929*n^4 +616*n^6 -96*n^7 +16*n^8)/2520 for n in (5..40)] # G. C. Greubel, Sep 29 2019
Formula
From G. C. Greubel, Sep 29 2019: (Start)
a(n) = Sum_{j=0..n-3} binomial(2*n-j, j+9), with a(4) = 1.
a(n) = Fibonacci(2*n+10) - (138600 +133530*n +63999*n^2 + 20286*n^3 + 5929*n^4 + 616*n^6 - 96*n^7 + 16*n^8)/2520.
G.f.: x^4*(1 - 2*x + 175*x^2 - 33*x^3 + 408*x^4 - 614*x^5 + 587*x^6 - 414*x^7 + 201*x^8 - 64*x^9 + 12*x^10 - x^11)/((1-x)^9*(1-3*x+x^2)). (End)
Extensions
Terms a(23) onward added by G. C. Greubel, Sep 29 2019