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A096386 Expansion of x^2(x^4+x^2+x+1)/(x^7-x^6-x+1). 0
0, 0, 1, 2, 3, 3, 4, 4, 5, 6, 7, 7, 8, 8, 9, 10, 11, 11, 12, 12, 13, 14, 15, 15, 16, 16, 17, 18, 19, 19, 20, 20, 21, 22, 23, 23, 24, 24, 25, 26, 27, 27, 28, 28, 29, 30, 31, 31, 32, 32, 33, 34, 35, 35, 36, 36, 37, 38, 39, 39, 40, 40, 41, 42, 43, 43, 44, 44, 45, 46, 47, 47, 48, 48 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

First differences are 6-periodic.

Number of numbers <= n which are divisible by 2 or 3. - Vladeta Jovovic, Mar 13 2007

REFERENCES

S. Ramanujan, Question 723, Collected Papers of Srinivasa Ramanujan, p. 332, Ed. G. H. Hardy et al., AMS Chelsea 2000.

LINKS

Table of n, a(n) for n=0..73.

S. Ramanujan, Question 723, J. Ind. Math. Soc.

Index entries for two-way infinite sequences

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

FORMULA

a(n) = [n/2] + [(n+3)/6] = [n/3] + [(n+2)/6] + [(n+4)/6].

G.f.: x^2(1+x+x^2+x^4)/((1-x)(1-x^6)).

a(-n) = -a(n-1)-1.

a(n) = 4 + a(n-6).

a(n) = Sum_{k=0..n} (1/90)*(-11*(k mod 6)+19*((k+1) mod 6)+4*((k+2) mod 6)+4*((k+3) mod 6)-11*((k+4) mod 6)+19*((k+5) mod 6)))-1. - Paolo P. Lava, Jun 25 2007

MATHEMATICA

CoefficientList[Series[x^2 (1 + x + x^2 + x^4)/((1 - x) (1 - x^6)), {x, 0, 73}], x] (* Michael De Vlieger, Apr 13 2016 *)

LinearRecurrence[{1, 0, 0, 0, 0, 1, -1}, {0, 0, 1, 2, 3, 3, 4}, 80] (* Harvey P. Dale, Jul 04 2016 *)

PROG

(PARI) a(n) = floor(n/2) + floor((n+3)/6)

(PARI) a(n)=n\2+(n+3)\6

CROSSREFS

Sequence in context: A309077 A057365 A014245 * A257063 A273663 A135671

Adjacent sequences:  A096383 A096384 A096385 * A096387 A096388 A096389

KEYWORD

nonn,easy

AUTHOR

Ralf Stephan, Aug 05 2004

STATUS

approved

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Last modified August 3 21:16 EDT 2021. Contains 346441 sequences. (Running on oeis4.)