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A055264
Possible values of A055263; numbers equal to 0, 1, 3 or 6 modulo 9.
7
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
REFERENCES
Albert H. Beiler, Recreations in the theory of numbers, New York, Dover, (2nd ed.) 1966. See p. 190.
FORMULA
a(n) = a(n-4) + 9 = 9*floor(n/4) + (n mod 4)*(1 + (n mod 4))/2.
G.f.: x*(1+2*x+3*x^2+3*x^3)/((1-x)^2*(1+x)*(1+x^2)). - R. J. Mathar, Sep 30 2008
E.g.f.: (3*cos(x) + (9*x - 3)*cosh(x) - sin(x) + (9*x - 4)*sinh(x))/4. - Stefano Spezia, Aug 07 2024
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
KEYWORD
easy,nonn,base
AUTHOR
Henry Bottomley, May 08 2000
STATUS
approved