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

Author

Mathew Munro, Oct 30 2018

Keywords

• nonn
• easy

Comments

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

Examples

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

Links

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

Crossrefs

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

Programs

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 *)

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

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

Extensions

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