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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).
1
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
0,4
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)
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 *)
PROG
(PARI) concat([0], vector(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
(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
(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
CROSSREFS
Sequence in context: A086968 A101824 A270238 * A348478 A363543 A242315
KEYWORD
nonn
STATUS
approved