A027956 a(n) = T(2n+1, n+4), T given by A027948.

1, 9, 175, 1518, 8735, 39130, 148487, 502415, 1568062, 4622488, 13091798, 36067176, 97522270, 260459265, 690141333, 1819657318, 4783398669, 12551942930, 32903246829, 86201363911, 225761428636, 591165917888, 1547848480940, 4052529200192, 10609936578716, 27777538280521

Offset: 3

Author

Clark Kimberling

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 3..1000
• Index entries for linear recurrences with constant coefficients, signature (11,-53,148,-266,322,-266,148,-53,11,-1).

Crossrefs

Cf. A000045, A027948.

Programs

GAP

Concatenation([1], List([4..40], n-> Fibonacci(2*n+10) -(34650 +33360*n +16065*n^2 +5089*n^3 +1260*n^4 +280*n^5 +16*n^7)/630) ); # G. C. Greubel, Sep 30 2019

Magma

[1] cat [Fibonacci(2*n+10) -(34650 +33360*n +16065*n^2 +5089*n^3 +1260*n^4 +280*n^5 +16*n^7)/630: n in [4..40]]; // G. C. Greubel, Sep 30 2019

Maple

with(combinat); seq(`if`(n=3,1, fibonacci(2*n+10) -(34650 +33360*n +16065*n^2 +5089*n^3 +1260*n^4 +280*n^5 +16*n^7)/630), n=3..40); # G. C. Greubel, Sep 30 2019

Mathematica

Table[If[n==3, 1, Fibonacci[2*n+10] -(34650 +33360*n +16065*n^2 +5089*n^3 +1260*n^4 +280*n^5 +16*n^7)/630], {n, 3, 40}] (* G. C. Greubel, Sep 30 2019 *)
LinearRecurrence[{11,-53,148,-266,322,-266,148,-53,11,-1},{1,9,175,1518,8735,39130,148487,502415,1568062,4622488,13091798},40] (* Harvey P. Dale, Sep 12 2021 *)

PARI

vector(40, n, my(m=n+2); if(m==3, 1, fibonacci(2*m+10) -(34650 +33360*m +16065*m^2 +5089*m^3 +1260*m^4 +280*m^5 +16*m^7)/630) ) \\ G. C. Greubel, Sep 30 2019

Sage

[1]+[fibonacci(2*n+10) -(34650 +33360*n +16065*n^2 +5089*n^3 +1260*n^4 +280*n^5 +16*n^7)/630 for n in (4..40)] # G. C. Greubel, Sep 30 2019

Formula

From G. C. Greubel, Sep 30 2019: (Start)

a(n) = Sum_{j=0..n-3} binomial(2*n-j+1, j+8) for n >= 4.

a(n) = Fibonacci(2*n+10) - (34650 +33360*n +16065*n^2 +5089*n^3 +1260*n^4 +280*n^5 +16*n^7)/630 for n >= 4.

G.f.: x^3*(1 -2*x +129*x^2 -78*x^3 +246*x^4 -329*x^5 +266*x^6 -148*x^7 +53*x^8 -11*x^9 +x^10)/((1-x)^8*(1-3*x+x^2)). (End)

Extensions

Name corrected and terms a(22) onward by G. C. Greubel, Sep 30 2019