A135056 Pentanacci numbers: a(n) = a(n-1) + a(n-2) + a(n-3) + a(n-4) + a(n-5) if n>=5, and a(n) = n otherwise.

0, 1, 2, 3, 4, 10, 20, 39, 76, 149, 294, 578, 1136, 2233, 4390, 8631, 16968, 33358, 65580, 128927, 253464, 498297, 979626, 1925894, 3786208, 7443489, 14633514, 28768731, 56557836, 111189778, 218593348, 429743207, 844852900

Offset: 0

Author

Artur Jasinski, Nov 15 2007, Nov 18 2007

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Piezas, Tito III and Weisstein, Eric W., Pentanacci Number.
• Index entries for linear recurrences with constant coefficients, signature (1,1,1,1,1).

Crossrefs

Cf. A001591, A135055.

Programs

Mathematica

a[n_] := a[n] = a[n - 1] + a[n - 2] + a[n - 3] + a[n - 4] + a[n - 5]; a[0] = 0; a[1] = 1; a[2] = 2; a[3] = 3; a[4] = 4; Table[a[n], {n, 0, 50}] (* Artur Jasinski, Nov 18 2007 *)
LinearRecurrence[{1,1,1,1,1},Range[0,4],40] (* Harvey P. Dale, Oct 18 2013 *)

Formula

G.f.: x*(x-1)*(2*x^2+2*x+1)/(-1+x^5+x^4+x^3+x^2+x). - Maksym Voznyy (voznyy(AT)mail.ru), Aug 12 2009