A280221 a(n) = (-2)^(n-1)*a(n-1) + a(n-2) with a(0) = 0 and a(1) = 1.

0, 1, -2, -7, 54, 857, -27370, -1750823, 224077974, 57362210521, -29369227708778, -30074031811578151, 61591587780884344470, 252279113476470463370969, -2066670436007658255050633578, -33860328171270359374279117170983

Offset: 0

Author

Seiichi Manyama, Dec 29 2016

Keywords

• sign

Examples

			G.f. = x - 2*x^2 - 7*x^3 + 54*x^4 + 857*x^5 - 27370*x^6 + ...
		

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..81

Crossrefs

Cf. similar sequences with the recurrence q^(n-1)*a(n-1) + a(n-2) for n>1, a(0)=0 and a(1)=1: A280222 (q=-3), this sequence (q=-2), A280261 (q=-1), A000045 (q=1), A015473 (q=2), A015474 (q=3), A015475 (q=4), A015476 (q=5), A015477 (q=6), A015479 (q=7), A015480 (q=8), A015481 (q=9), A015482 (q=10), A015484 (q=11).

Programs

Magma

I:=[1,-2]; [0] cat [n le 2 select I[n] else (-2)^(n-1)*Self(n-1) +Self(n-2): n in [1..30]]; // G. C. Greubel, Oct 13 2018

Mathematica

a[n_] := (-2)^(n -1) a[n -1] + a[n -2]; a[0] = 0; a[1] = 1; Array[a, 16, 0] (* Robert G. Wilson v, Dec 29 2016 *)

PARI

m=30; v=concat([1, -2], vector(m-2)); for(n=3, m, v[n] = (-2)^(n-1)*v[n-1] + v[n-2]); concat([0],v) \\ G. C. Greubel, Oct 13 2018

Ruby

def A(m, n)
  i, a, b = 0, 0, 1
  ary = [0]
  while i < n
    i += 1
    a, b = b, b * m ** i + a
    ary << a
  end
  ary
end
def A280221(n)
  A(-2, n)
end