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A251655
4-step Fibonacci sequence starting with 0, 1, 1, 1.
5
0, 1, 1, 1, 3, 6, 11, 21, 41, 79, 152, 293, 565, 1089, 2099, 4046, 7799, 15033, 28977, 55855, 107664, 207529, 400025, 771073, 1486291, 2864918, 5522307, 10644589, 20518105, 39549919, 76234920, 146947533, 283250477, 545982849, 1052415779, 2028596638
OFFSET
0,5
FORMULA
a(n+4) = a(n) + a(n+1) + a(n+2) + a(n+3).
MATHEMATICA
LinearRecurrence[Table[1, {4}], {0, 1, 1, 1}, 36] (* Michael De Vlieger, Dec 09 2014 *)
PROG
(J) (see www.jsoftware.com) First construct the generating matrix
[M=: (#.@}: + {:)\"1&.|: <:/~i.4
1 1 1 1
1 2 2 2
2 3 4 4
4 6 7 8
Given that matrix, one can produce the first 4*250 numbers with
, M(+/ . *)^:(i.250) 0 1 1 1x
CROSSREFS
Other 4-step Fibonacci sequences are A000078, A000288, A001630, A001631, A001648, A073817, A100532, A251654, A251656, A251672, A251703, A251704, A251705.
Sequence in context: A291408 A202012 A261392 * A132658 A293320 A024495
KEYWORD
nonn,easy
AUTHOR
Arie Bos, Dec 06 2014
STATUS
approved