A321025 a(n) = sum of a(n-4) and a(n-5), with the lowest possible initial values that will generate a sequence where a(n) is always > a(n-1): 4, 5, 6, 7 and 8.

4, 5, 6, 7, 8, 9, 11, 13, 15, 17, 20, 24, 28, 32, 37, 44, 52, 60, 69, 81, 96, 112, 129, 150, 177, 208, 241, 279, 327, 385, 449, 520, 606, 712, 834, 969, 1126, 1318, 1546, 1803, 2095, 2444, 2864, 3349, 3898, 4539, 5308, 6213, 7247, 8437, 9847, 11521, 13460, 15684

Offset

1,1

Comments

A sum of prior terms in the sequence, like the Fibonacci and Padovan sequences.

Links

Table of n, a(n) for n=1..54.

Index entries for linear recurrences with constant coefficients, signature (0,0,0,1,1).

Formula

a(n) = a(n-4) + a(n-5) with a(1) = 4, a(2) = 5, a(3) = 6, a(4) = 7 and a(5) = 8.

G.f.: x*(4 + 5*x + 6*x^2 + 7*x^3 + 4*x^4)/(1 - x^4 - x^5). - Andrew Howroyd, Oct 31 2018

Example

a(6) = a(6-4) + a(6-5) = a(2) + a(1) = 5 + 4 = 9.

Mathematica

Rest@ CoefficientList[Series[x (4 + 5 x + 6 x^2 + 7 x^3 + 4 x^4)/(1 - x^4 - x^5), {x, 0, 54}], x] (* Michael De Vlieger, Oct 31 2018 *)

Prog

(PARI) a(n) = if(n<=5, n+3, a(n-4) + a(n-5)); \\ Michel Marcus, Oct 31 2018
(PARI) Vec((4 + 5*x + 6*x^2 + 7*x^3 + 4*x^4)/(1 - x^4 - x^5) + O(x^50)) \\ Andrew Howroyd, Oct 31 2018

Crossrefs

Cf. A000045, A000931, A079398, A164317, A103372, A103373

Sequence in context: A120181 A016070 A299536 * A047569 A039062 A067187

Adjacent sequences: A321022 A321023 A321024 * A321026 A321027 A321028

Keyword

nonn,easy

Author

Mathew Munro, Oct 30 2018

Extensions

a(19), a(20) corrected by Georg Fischer, May 24 2019

Status

approved