A251653 5-step Fibonacci sequence starting with 0,0,1,0,0.

0, 0, 1, 0, 0, 1, 2, 4, 7, 14, 28, 55, 108, 212, 417, 820, 1612, 3169, 6230, 12248, 24079, 47338, 93064, 182959, 359688, 707128, 1390177, 2733016, 5372968, 10562977

Offset

0,7

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

H. Prodinger, Counting Palindromes According to r-Runs of Ones Using Generating Functions, J. Int. Seq. 17 (2014) # 14.6.2, even length, r=4.

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

Formula

a(n+5) = a(n) + a(n+1) + a(n+2) + a(n+3) + a(n+4).

G.f.: x^2*(x^2 + x - 1)/(x^5 + x^4 + x^3 + x^2 + x - 1). - Chai Wah Wu, May 27 2016

Mathematica

LinearRecurrence[{1, 1, 1, 1, 1}, {0, 0, 1, 0, 0}, 100] (* G. C. Greubel, May 27 2016 *)

Prog

(J) (see www.jsoftware.com) First construct the generating matrix
1  1  1  1  1
1  2  2  2  2
2  3  4  4  4
4  6  7  8  8
8 12 14 15 16
Given that matrix one can produce the first 5*200 numbers by
, M(+/ . *)^:(i.250) 0 0 1 0 0x

Crossrefs

Other 5-step sequences are A000322, A001591, A023424, A074048, A124312, A124313, A122997, A135055, A135056, A145029

Sequence in context: A068060 A239791 A358837 * A057744 A251708 A293325

Adjacent sequences: A251650 A251651 A251652 * A251654 A251655 A251656

Keyword

nonn,easy

Author

Arie Bos, Dec 06 2014

Status

approved