A137166 Sequence equals its 4th differences shifted by one index.

1, 3, 7, 15, 32, 70, 156, 349, 778, 1728, 3833, 8505, 18884, 41943, 93160, 206897, 459459, 1020311, 2265815, 5031792, 11174374, 24815508, 55108933, 122382762, 271780616, 603555049, 1340341377, 2976555532, 6610168495, 14679492624

Offset

0,2

Comments

Binomial transform yields A079398 without the initial (0,1,1,1). - R. J. Mathar, Apr 09 2008

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (4,-6,5,-1).

Formula

a(n) = 4*a(n-1)-6*a(n-2)+5*a(n-3)-a(n-4). - R. J. Mathar, Apr 09 2008

G.f.: (x^2 - x + 1) / (x^4 - 5*x^3 + 6*x^2 - 4*x + 1). - Alexander R. Povolotsky, Apr 08 2008

Mathematica

s = ""; a = 0; b = 1; c = 1; d = 1; For[i = 0, i < 23, a = a + b; s = s <> ToString[a] <> ", "; b = b + c; c = c + d; d = d + a; i++ ]; Print[s]
LinearRecurrence[{4, -6, 5, -1}, {1, 3, 7, 15}, 40] (* Vincenzo Librandi, Jun 15 2013 *)

Prog

(Magma) [n le 4 select 2^n-1 else 4*Self(n-1)-6*Self(n-2)+5*Self(n-3)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Jun 15 2013
(PARI) a(n)=([0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1; -1, 5, -6, 4]^n*[1; 3; 7; 15])[1, 1] \\ Charles R Greathouse IV, Oct 03 2016

Crossrefs

Cf. A079398.

Sequence in context: A099444 A374678 A132402 * A101890 A307573 A134195

Adjacent sequences: A137163 A137164 A137165 * A137167 A137168 A137169

Keyword

nonn,easy

Author

Vladimir Joseph Stephan Orlovsky, Apr 03 2008

Extensions

Edited by R. J. Mathar, Apr 09 2008

Edited by Bruno Berselli, Apr 07 2011

Status

approved