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

Author

Vladimir Joseph Stephan Orlovsky, Apr 03 2008

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A079398.

Programs

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

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 *)

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

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

Extensions

Edited by R. J. Mathar, Apr 09 2008

Edited by Bruno Berselli, Apr 07 2011