

A321025


a(n) = sum of a(n4) and a(n5), with the lowest possible initial values that will generate a sequence where a(n) is always > a(n1): 4, 5, 6, 7 and 8.


0



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
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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(n4) + a(n5) 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(64) + a(65) = 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(n4) + a(n5)); \\ 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



