A027958 a(n) = T(n,m) + T(n,m+1) + ... + T(n,n), where m = floor((n+2)/2), T given by A027948.

1, 1, 4, 5, 20, 32, 95, 169, 424, 793, 1816, 3488, 7583, 14789, 31172, 61357, 126892, 251200, 513343, 1019921, 2068496, 4119281, 8313584, 16580800, 33358015, 66594637, 133703500, 267089189, 535524644, 1070217248, 2143959071

Offset: 1

Author

Clark Kimberling

Keywords

• nonn

Comments

a(n) is the sum of the terms of the 2nd half of the n-th row of the A027948 triangle. - Michel Marcus, Oct 01 2019

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (2,4,-8,-4,8,1,-2).

Crossrefs

Cf. A000045, A027948.

Programs

GAP

F:=Fibonacci;; List([1..40], n-> (3 +(-1)^n +2^(n+1) -(-1)^n*F(n+1) -F(n+4))/2); # G. C. Greubel, Sep 30 2019

Magma

F:=Fibonacci; [(3 +(-1)^n +2^(n+1) -(-1)^n*F(n+1) -F(n+4))/2: n in [1..40]]; // G. C. Greubel, Sep 30 2019

Maple

f:= combinat[fibonacci]: seq((3 +(-1)^n +2^(n+1) -(-1)^n*f(n+1) -f(n+4))/2, n=1..40); # G. C. Greubel, Sep 30 2019

Mathematica

Table[(3 +(-1)^n +2^(n+1) -(-1)^n*Fibonacci[n+1] -Fibonacci[n+4])/2, {n,40}] (* G. C. Greubel, Sep 30 2019 *)

PARI

vector(40, n, f=fibonacci; (3 +(-1)^n +2^(n+1) -(-1)^n*f(n+1) -f(n+4))/2 ) \\ G. C. Greubel, Sep 30 2019

Sage

f=fibonacci; [(3 +(-1)^n +2^(n+1) -(-1)^n*f(n+1) -f(n+4))/2 for n in (1..40)] # G. C. Greubel, Sep 30 2019

Formula

G.f.: x*(1 -x -2*x^2 + x^3 +6*x^4 -2*x^6)/((1-2*x)*(1-x^2)(1+x-x^2)*(1-x-x^2)).

a(n) = (3 +(-1)^n +2^(n+1) -(-1)^n*Fibonacci(n+1) -Fibonacci(n+4))/2. - G. C. Greubel, Sep 30 2019