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A111651 n appears 3n times. 2
1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

Ramanujan theta functions: f(q) := Prod_{k>=1} (1-(-q)^k) (see A121373), phi(q) := theta_3(q) := Sum_{k=-oo..oo} q^(k^2) (A000122), psi(q) := Sum_{k=0..oo} q^(k*(k+1)/2) (A010054), chi(q) := Prod_{k>=0} (1+q^(2k+1)) (A000700).

LINKS

Table of n, a(n) for n=1..105.

Michael Somos, Introduction to Ramanujan theta functions

Eric Weisstein's World of Mathematics, Ramanujan Theta Functions

FORMULA

a(n) = nearest integer to cube root of n. - Jonathan Vos Post, Sep 06 2006

Expansion of (q/(1-q))psi(q^3) in powers of q where psi() is a Ramanujan theta function. - Michael Somos, Aug 31 2006

G.f.: x/(1-x)*Product_{k>0} (1-x^(3k))^((-1)^k).

MATHEMATICA

Table[PadRight[{}, 3n, n], {n, 10}]//Flatten (* Harvey P. Dale, Sep 15 2021 *)

PROG

(PARI) {a(n)=if(n<1, 0, polcoeff( x/(1-x)*prod(k=1, n\3, (1-x^(3*k))^(-1)^k, 1+O(x^n)), n))} /* Michael Somos, Aug 31 2006 */

CROSSREFS

Cf. A000194, A008585, A111650, A111652.

Sequence in context: A340763 A286103 A056556 * A151982 A259361 A111854

Adjacent sequences:  A111648 A111649 A111650 * A111652 A111653 A111654

KEYWORD

easy,nonn

AUTHOR

Jonathan Vos Post, Aug 12 2005

STATUS

approved

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Last modified May 25 21:44 EDT 2022. Contains 354071 sequences. (Running on oeis4.)