A214885 a(n) = Sum_{k=0..n} (-1)^k*F(k)*F(k+3), where F=A000045 (Fibonacci numbers).

0, -3, 2, -14, 25, -80, 192, -523, 1346, -3550, 9265, -24288, 63552, -166419, 435650, -1140590, 2986057, -7817648, 20466816, -53582875, 140281730, -367262398, 961505377, -2517253824, 6590256000, -17253514275, 45170286722, -118257345998

Offset

0,2

Comments

This is the m=3 member of the m-family b(m,n) given in a comment on A214884, where also the formula and the o.g.f. are found.

Links

Table of n, a(n) for n=0..27.

Formula

a(n) = b(3,n) = 2*A119283(n) + (-1)^n*A001654(n), n >= 0.

O.g.f.: A(3,x) = -x*(3+x)/((1-x)^2*(1+3*x+x^2)). See the comment above.

a(n) = ((-1)^n*Fibonacci(2*n + 4) - 4*n - 3)/5. - Ehren Metcalfe, Aug 21 2017

Mathematica

Table[Sum[(-1)^k*Fibonacci[k]*Fibonacci[k + 3], {k, 0, n}], {n, 0, 27}] (* Michael De Vlieger, Aug 23 2017 *)

Crossrefs

Cf. A119283, -A077916(n-1), A214884.

Sequence in context: A231183 A324661 A163355 * A145747 A055234 A291051

Adjacent sequences: A214882 A214883 A214884 * A214886 A214887 A214888

Keyword

sign,easy

Author

Wolfdieter Lang, Jul 30 2012

Status

approved