OFFSET
1,1
COMMENTS
Numbers == {13, 31, 49, 67} mod 90 with additive sum sequence 13{+18+18+18+36} {repeat ...}. Includes all prime numbers > 5 with digital root 4.
LINKS
Colin Barker, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1).
FORMULA
Numbers == {13, 31, 49, 67} mod 90.
From Colin Barker, Mar 25 2018: (Start)
G.f.: x*(13 + 18*x + 18*x^2 + 18*x^3 + 23*x^4) / ((1 - x)^2*(1 + x)*(1 + x^2)).
a(n) = a(n-1) + a(n-4) - a(n-5) for n>5.
(End)
MATHEMATICA
Rest@ CoefficientList[Series[x (13 + 18 x + 18 x^2 + 18 x^3 + 23 x^4)/((1 - x)^2*(1 + x) (1 + x^2)), {x, 0, 50}], x] (* Michael De Vlieger, Apr 21 2018 *)
LinearRecurrence[{1, 0, 0, 1, -1}, {13, 31, 49, 67, 103}, 50] (* Harvey P. Dale, May 11 2019 *)
PROG
(PARI) Vec(x*(13 + 18*x + 18*x^2 + 18*x^3 + 23*x^4) / ((1 - x)^2*(1 + x)*(1 + x^2)) + O(x^60)) \\ Colin Barker, Mar 25 2018
(GAP) Filtered(Filtered([1..1200], n->n mod 2 <> 0 and n mod 3 <> 0 and n mod 5 <> 0), i->i-9*Int((i-1)/9)=4); # Muniru A Asiru, Apr 22 2018
CROSSREFS
KEYWORD
nonn,base,easy
AUTHOR
Gary Croft, Mar 24 2018
EXTENSIONS
Last term corrected by Colin Barker, Mar 25 2018
STATUS
approved