A027946 a(n) is the sum of the non-Fibonacci numbers in row n of array T given by A027935, computed as T(n,m) + T(n,m+1) + ... + T(n,n-1), where m = floor((n+2)/2).

0, 0, 0, 4, 7, 23, 42, 106, 200, 456, 879, 1903, 3718, 7814, 15396, 31780, 62951, 128487, 255378, 517522, 1030864, 2079440, 4147935, 8342239, 16655822, 33433038, 66791052, 133899916, 267603415, 536038871, 1071563514, 2145305338

Offset: 0

Author

Clark Kimberling

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (3,1,-9,5,3,-2).

Crossrefs

Cf. A000045, A027935.

Programs

GAP

Concatenation([0], List([1..40], n-> (2^(n+1)-2-Fibonacci(n+3) -(-1)^n*Fibonacci(n))/2)); # G. C. Greubel, Sep 28 2019

Magma

[0] cat [(2^(n+1)-2-Fibonacci(n+3) -(-1)^n*Fibonacci(n))/2: n in [1..40]]; // G. C. Greubel, Sep 28 2019

Maple

with(combinat); seq(`if`(n=0,0, (2^(n+1)-2-fibonacci(n+3) -(-1)^n* fibonacci(n))/2), n=0..40); # G. C. Greubel, Sep 28 2019

Mathematica

Table[If[n==0,0,(2^(n+1) -2 -Fibonacci[n+3] -(-1)^n*Fibonacci[n])/2], {n, 0, 40}] (* G. C. Greubel, Sep 28 2019 *)

PARI

concat([0], vector(40, n, (2^(n+1)-2-fibonacci(n+3) -(-1)^n* fibonacci(n))/2)) \\ G. C. Greubel, Sep 28 2019

Sage

[0]+[(2^(n+1)-2-fibonacci(n+3) -(-1)^n*fibonacci(n))/2 for n in (1..40)] # G. C. Greubel, Sep 28 2019

Formula

G.f.: x^3*(4 - 5*x - 2*x^2 + 2*x^3)/((1-x)*(1-2*x)*(1+x-x^2)*(1-x-x^2)).

From G. C. Greubel, Sep 28 2019: (Start)

a(n) = (2^(n+1) - 2 - Fibonacci(n+3) - (-1)^n*Fibonacci(n))/2, n > 0.

a(2*n) = 4^n - 1 - Fibonacci(2*n+2), n > 0.

a(2*n+1) = 2^(2*n+1) - 1 - Fibonacci(2*n+2). (End)