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

4,2

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).

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)

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

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 *)

Prog

(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
(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
(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
(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

Crossrefs

Cf. A000045, A027948.

Sequence in context: A302095 A276019 A004702 * A056602 A349731 A239772

Adjacent sequences: A027949 A027950 A027951 * A027953 A027954 A027955

Keyword

nonn

Author

Clark Kimberling

Extensions

Terms a(23) onward added by G. C. Greubel, Sep 29 2019

Status

approved