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A264147 a(n) = n*F(n+1) - (n+1)*F(n), where F = A000045. 1
0, -1, 1, 1, 5, 10, 22, 43, 83, 155, 285, 516, 924, 1639, 2885, 5045, 8773, 15182, 26162, 44915, 76855, 131119, 223101, 378696, 641400, 1084175, 1829257, 3081193, 5181893, 8702290, 14594830, 24446971, 40902299, 68359619, 114132765, 190373580, 317258388, 528265207 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

a(n) is prime for n = 4, 7, 8, 26, 28, 52, 86, 87, 93, 97, 158, 196, 303, 2908, 3412, 4111, 4208, 6183, 6337, 9878, ...

LINKS

Bruno Berselli, Table of n, a(n) for n = 0..500

Index entries for linear recurrences with constant coefficients, signature (2,1,-2,-1).

FORMULA

G.f.:  x*(-1 + 3*x)/(1 - x - x^2)^2.

a(n) = 2*a(n-1) + a(n-2) - 2*a(n-3) - a(n-4).

a(n) = n*F(n-1) - F(n).

a(n) = Sum_{i=0..n} F(i)*L(n-1-i), where L() is a Lucas number (A000032).

a(n) = 3*A001629(n) - A001629(n+1).

a(n) = -(-1)^n*A178521(-n).

a(n+2) - a(n) = A007502(n+1).

Sum_{i>0} 1/a(i) = 1.39516607051636028893879220294180374...

a(n) = (-((1+sqrt(5))/2)^n*(2*sqrt(5) + (-5+sqrt(5))*n) + ((1-sqrt(5))/2)^n*(2*sqrt(5) + (5+sqrt(5))*n)) / 10. - Colin Barker, Jul 27 2017

MATHEMATICA

Table[n Fibonacci[n + 1] - (n + 1) Fibonacci[n], {n, 0, 40}]

PROG

(PARI) for(n=0, 40, print1(n*fibonacci(n+1)-(n+1)*fibonacci(n)", "));

(Sage) [n*fibonacci(n+1)-(n+1)*fibonacci(n) for n in (0..40)]

(Maxima) makelist(n*fib(n+1)-(n+1)*fib(n), n, 0, 40);

(MAGMA) [n*Fibonacci(n+1)-(n+1)*Fibonacci(n): n in [0..40]];

(PARI) concat(0, Vec(-x*(1 - 3*x) / (1 - x - x^2)^2 + O(x^50))) \\ Colin Barker, Jul 27 2017

CROSSREFS

Cf. A000045, A001629, A007502.

Cf. A178521: n*F(n+1) + (n+1)*F(n).

Cf. A094588: n*F(n-1) + F(n).

Cf. A099920: Sum_{i=0..n} F(i)*L(n-i).

Cf. A023607: Sum_{i=0..n} F(i)*L(n+1-i).

Sequence in context: A271257 A087746 A064694 * A229440 A067622 A196240

Adjacent sequences:  A264144 A264145 A264146 * A264148 A264149 A264150

KEYWORD

sign,easy

AUTHOR

Bruno Berselli, Nov 04 2015

STATUS

approved

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Last modified March 7 12:19 EST 2021. Contains 341885 sequences. (Running on oeis4.)