OFFSET
1,1
COMMENTS
A007310(a(n)+1) is always a multiple of 13.
a(n) mod 6 follows the following pattern: 4,3,0,5,2,1,4,3,0,5,2,1 and so on.
a(n) mod 4 = A010873(n)
A020639(A007310(a(n)+1) = 5 when n is congruent to 2 or 9 (mod 10) (n is a term in A273669). It equals 7 when n is congruent to 3 or 12 (mod 14) but not congruent to 2 or 9 (mod 10). It equals 11 when n is congruent to 4 or 19 (mod 22) but not congruent to 2 or 9 (mod 10) and not congruent to 3 or 12 (mod 14). Otherwise, it is 13.
LINKS
Davis Smith, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (1,1,-1).
FORMULA
a(n) = 13*n - A010720(n+1).
From Colin Barker, Feb 08 2019: (Start)
G.f.: x*(4 + 17*x + 5*x^2) / ((1 - x)^2*(1 + x)).
a(n) = 13*n - 5 for n even.
a(n) = 13*n - 9 for n odd.
a(n) = a(n-1) + a(n-2) - a(n-3) for n>3. (End)
E.g.f.: 5 + (13*x - 7)*exp(x) + 2*exp(-x). - David Lovler, Sep 09 2022
MAPLE
seq(seq(26*i+j, j=[4, 21]), i=0..200);
MATHEMATICA
Select[Range[200], MemberQ[{4, 21}, Mod[#, 26]] &]
PROG
(PARI) for(n=1, 1000, if((n%26==4) || (n%26==21), print1(n, ", ")))
(PARI) Vec(x*(4 + 17*x + 5*x^2) / ((1 - x)^2*(1 + x)) + O(x^40)) \\ Colin Barker, Feb 08 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Davis Smith, Feb 03 2019
STATUS
approved