OFFSET
0,3
COMMENTS
Note that these numbers should be read in base n. For instance, a(19) = 100 is actually (10)(00) in base 19, which equals 190 (the 19th triangular number) in base 10. - T. D. Noe, Feb 01 2013
LINKS
Harry J. Smith, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (0,2,0,-1).
FORMULA
Apart from a(1), a(2n-1) = 10n and a(2n) = 11n.
From Colin Barker, Feb 01 2013: (Start)
a(n) = (-10*(-1+(-1)^n)+(21+(-1)^n)*n)/4 for n>1.
a(n) = 2*a(n-2)-a(n-4) for n>5.
G.f.: -x*(9*x^4-18*x^2-11*x-1) / ((x-1)^2*(x+1)^2). (End)
EXAMPLE
a(3) = 1 + 2 + 3 = 6 = 20_3.
MATHEMATICA
Join[{0, 1}, Table[FromDigits[IntegerDigits[n*(n+1)/2, n]], {n, 2, 50}]] (* T. D. Noe, Feb 01 2013 *)
Join[{0, 1}, LinearRecurrence[{0, 2, 0, -1}, {11, 20, 22, 30}, 60]] (* Vincenzo Librandi, Jan 04 2016 *)
PROG
(PARI) baseE(x, b)= { local(d, e=0, f=1); if (b<2, return(x)); while (x>0, d=x%b; x\=b; e+=d*f; f*=10); return(e) } { for (n=0, 1000, write("b053715.txt", n, " ", baseE(n*(n + 1)/2, n)) ) } \\ Harry J. Smith, Apr 27 2010
(Magma) I:=[0, 1, 11, 20, 22, 30]; [n le 6 select I[n] else 2*Self(n-2)-Self(n-4): n in [1..60]]; // Vincenzo Librandi, Jan 04 2016
CROSSREFS
KEYWORD
base,easy,nonn
AUTHOR
Henry Bottomley, Feb 10 2000
EXTENSIONS
More terms from James A. Sellers, Feb 22 2000
STATUS
approved