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A053715 a(n) = n-th triangular number (the sum of the first n integers) in base n. 1
0, 1, 11, 20, 22, 30, 33, 40, 44, 50, 55, 60, 66, 70, 77, 80, 88, 90, 99, 100, 110, 110, 121, 120, 132, 130, 143, 140, 154, 150, 165, 160, 176, 170, 187, 180, 198, 190, 209, 200, 220, 210, 231, 220, 242, 230, 253, 240, 264, 250, 275, 260, 286, 270, 297, 280 (list; graph; refs; listen; history; text; internal format)
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

Cf. A000217.

Sequence in context: A124251 A279431 A230541 * A250203 A339307 A038581

Adjacent sequences:  A053712 A053713 A053714 * A053716 A053717 A053718

KEYWORD

base,easy,nonn

AUTHOR

Henry Bottomley, Feb 10 2000

EXTENSIONS

More terms from James A. Sellers, Feb 22 2000

STATUS

approved

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Last modified March 2 06:48 EST 2021. Contains 341744 sequences. (Running on oeis4.)