OFFSET
0,3
COMMENTS
This is the digital root sequence for A007588 and for A006003, two nice sequences relating to structured numbers (hexagonal anti-diamond numbers (vertex structure 13) and trigonal diamond numbers (vertex structure 4) respectively).
It is composed of all 9 of the nonzero digits, period 9. Root digits increase by 1 in sets of 3 [i.e., "5, 6, 7", "2, 3, 4" and "8, 9, 1"]. - Peter M. Chema, Aug 21 2016
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,1).
FORMULA
From Colin Barker, Jan 10 2016: (Start)
a(n) = a(n-9) for n>9.
G.f.: x*(1+5*x+6*x^2+7*x^3+2*x^4+3*x^5+4*x^6+8*x^7+9*x^8) / ((1-x)*(1+x+x^2)*(1+x^3+x^6)).
(End)
MATHEMATICA
FixedPoint[Total@ IntegerDigits@ # &, #] & /@ Table[n (2 n^2 - 1), {n, 0, 108}] (* Michael De Vlieger, Jan 09 2016 *)
PROG
(PARI) A010888(n)=if(n, (n-1)%9+1);
a(n) = A010888(n*(2*n^2 - 1)); \\ Michel Marcus, Jan 10 2016
(PARI) concat(0, Vec(x*(1+5*x+6*x^2+7*x^3+2*x^4+3*x^5+4*x^6+8*x^7+9*x^8) / ((1-x)*(1+x+x^2)*(1+x^3+x^6)) + O(x^100))) \\ Colin Barker, Jan 10 2016
CROSSREFS
KEYWORD
nonn,base,easy
AUTHOR
Peter M. Chema, Jan 08 2016
STATUS
approved