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A271833 Expansion of (1 + 2*x + 2*x^2 + 2*x^3 - 5*x^4 + 2*x^5 + 2*x^6 + 2*x^7)/((1 - x)^2*(1 + x + x^2 + x^3 + x^4 + x^5 + x^6 + x^7)). 1
1, 3, 5, 7, 2, 4, 6, 8, 9, 11, 13, 15, 10, 12, 14, 16, 17, 19, 21, 23, 18, 20, 22, 24, 25, 27, 29, 31, 26, 28, 30, 32, 33, 35, 37, 39, 34, 36, 38, 40, 41, 43, 45, 47, 42, 44, 46, 48, 49, 51, 53, 55, 50, 52, 54, 56, 57, 59, 61, 63, 58, 60, 62, 64, 65, 67, 69, 71, 66, 68, 70, 72, 73, 75, 77 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

4 consecutive odds, 4 consecutive evens.

LINKS

Table of n, a(n) for n=0..74.

Ilya Gutkovskiy, Illustration of initial terms

Index entries for sequences that are permutations of the natural numbers

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

FORMULA

G.f.: (1 + 2*x + 2*x^2 + 2*x^3 - 5*x^4 + 2*x^5 + 2*x^6 + 2*x^7)/((1 - x)^2*(1 + x + x^2 + x^3 + x^4 + x^5 + x^6 + x^7)).

a(n) = a(n-1) + a(n-8) - a(n-9).

a(n) = 1 + 2*n + 6*floor(n/8) - 7*floor(n/4). - Vaclav Kotesovec, Apr 15 2016

MATHEMATICA

CoefficientList[Series[(1 + 2 x + 2 x^2 + 2 x^3 - 5 x^4 + 2 x^5 + 2 x^6 + 2 x^7)/((1 - x)^2 (1 + x + x^2 + x^3 + x^4 + x^5 + x^6 + x^7)), {x, 0, 75}], x]

LinearRecurrence[{1, 0, 0, 0, 0, 0, 0, 1, -1}, {1, 3, 5, 7, 2, 4, 6, 8, 9}, 75]

PROG

(PARI) x='x+O('x^99); Vec((1+2*x+2*x^2+2*x^3-5*x^4+2*x^5+2*x^6+2*x^7)/((1-x)^2*(1+x+x^2+x^3+x^4+x^5+x^6+x^7))) \\ Altug Alkan, Apr 15 2016

CROSSREFS

Cf. A000027, A116966, A131793.

Sequence in context: A084763 A179650 A131214 * A104260 A263792 A263411

Adjacent sequences:  A271830 A271831 A271832 * A271834 A271835 A271836

KEYWORD

nonn,easy

AUTHOR

Ilya Gutkovskiy, Apr 15 2016

STATUS

approved

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Last modified January 16 23:44 EST 2019. Contains 319206 sequences. (Running on oeis4.)