A145029 Pentanacci numbers: a(n)=a(n-1)+a(n-2)+a(n-3)+a(n-4)+a(n-5), {1,2,3,4,5...}.

1, 2, 3, 4, 5, 15, 29, 56, 109, 214, 423, 831, 1633, 3210, 6311, 12408, 24393, 47955, 94277, 185344, 364377, 716346, 1408299, 2768643, 5443009, 10700674, 21036971, 41357596, 81306893, 159845143, 314247277, 617793880, 1214550789, 2387743982

Offset

1,2

Links

Table of n, a(n) for n=1..34.

Robbert Fokkink and Gandhar Joshi, Anti-recurrence sequences, arXiv:2506.13337 [math.NT], 2025. See p. 11.

Index entries for linear recurrences with constant coefficients, signature (1,1,1,1,1).

Formula

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

Mathematica

a=1; b=2; c=3; d=4; e=5; lst={a, b, c, d, e}; Do[f=a+b+c+d+e; AppendTo[lst, f]; a=b; b=c; c=d; d=e; e=f, {n, 5!}]; lst
LinearRecurrence[{1, 1, 1, 1, 1}, Range[5], 40](* Harvey P. Dale, Jun 20 2015 *)

Prog

(PARI) a(n)=([0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1; 1, 1, 1, 1, 1]^(n-1)*[1; 2; 3; 4; 5])[1, 1] \\ Charles R Greathouse IV, Jun 03 2026

Crossrefs

Sequence in context: A096774 A201356 A183528 * A145030 A242948 A102738

Adjacent sequences: A145026 A145027 A145028 * A145030 A145031 A145032

Keyword

nonn,easy

Author

Vladimir Joseph Stephan Orlovsky, Sep 30 2008

Extensions

G.f. proposed by Maksym Voznyy checked and corrected by R. J. Mathar, Sep 16 2009

Status

approved