A055264 Possible values of A055263; numbers equal to 0, 1, 3 or 6 modulo 9.

0, 1, 3, 6, 9, 10, 12, 15, 18, 19, 21, 24, 27, 28, 30, 33, 36, 37, 39, 42, 45, 46, 48, 51, 54, 55, 57, 60, 63, 64, 66, 69, 72, 73, 75, 78, 81, 82, 84, 87, 90, 91, 93, 96, 99, 100, 102, 105, 108, 109, 111, 114, 117, 118, 120, 123, 126, 127, 129, 132, 135, 136, 138, 141

Offset

0,3

Comments

The terms are the possible digit sums of a triangular number. - Amarnath Murthy, Jan 09 2002

Links

Table of n, a(n) for n=0..63.

Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1).

Formula

a(n) = a(n-4) + 9 = 9*floor(n/4) + (n mod 4)*(1 + (n mod 4))/2.

G.f.: x(1+2x+3x^2+3x^3)/((1-x)^2(1+x)(1+x^2)). - R. J. Mathar, Sep 30 2008

Mathematica

Select[Range[0, 200], MemberQ[{0, 1, 3, 6}, Mod[#, 9]]&] (* Harvey P. Dale, Apr 10 2014 *)
#+{0, 1, 3, 6}&/@(9*Range[0, 20])//Flatten (* Harvey P. Dale, Jun 03 2019 *)

Prog

(Python)
def A055264(n): return (0, 1, 3, 6)[n&3]+9*(n>>2) # Chai Wah Wu, Jan 30 2023

Crossrefs

Cf. A055263.

Sequence in context: A176423 A055632 A133006 * A113502 A229307 A356453

Adjacent sequences: A055261 A055262 A055263 * A055265 A055266 A055267

Keyword

easy,nonn,base

Author

Henry Bottomley, May 08 2000

Status

approved