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A263313 Permutation of the nonnegative integers: [4k+3, 4k, 4k+1, 4k+2, ...]. 1
3, 0, 1, 2, 7, 4, 5, 6, 11, 8, 9, 10, 15, 12, 13, 14, 19, 16, 17, 18, 23, 20, 21, 22, 27, 24, 25, 26, 31, 28, 29, 30, 35, 32, 33, 34, 39, 36, 37, 38, 43, 40, 41, 42, 47, 44, 45, 46, 51, 48, 49, 50, 55, 52, 53, 54, 59, 56, 57, 58, 63, 60, 61, 62, 67, 64, 65 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Table of n, a(n) for n=0..66.

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

FORMULA

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

a(n) = a(n-1)+a(n-4)-a(n-5) for n>4.

a(n) = n+1-2*(-1)^((n+1)*(n+2)*(n+3)/2).

a(2n) = A166519(n), a(2n+1) = A005843(n).

MAPLE

A263313:=n->n+1-2*(-1)^((n+1)*(n+2)*(n+3)/2): seq(A263313(n), n=0..100);

MATHEMATICA

Table[n + 1 - 2*(-1)^((n + 1)*(n + 2)*(n + 3)/2), {n, 0, 100}] (* or *) CoefficientList[Series[(3 - 3*x + x^2 + x^3 + 2*x^4)/((x - 1)^2*(1 + x + x^2 + x^3)), {x, 0, 100}], x]

PROG

(MAGMA) [n+1-2*(-1)^((n+1)*(n+2)*(n+3) div 2) : n in [0..100]];

(PARI) Vec((3-3*x+x^2+x^3+2*x^4)/((x-1)^2*(1+x+x^2+x^3)) + O(x^100)) \\ Altug Alkan, Oct 19 2015

CROSSREFS

Cf. A005843, A166519.

Sequence in context: A014573 A067166 A125209 * A071818 A014513 A144388

Adjacent sequences:  A263310 A263311 A263312 * A263314 A263315 A263316

KEYWORD

nonn,easy

AUTHOR

Wesley Ivan Hurt, Oct 19 2015

STATUS

approved

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Last modified April 19 16:18 EDT 2019. Contains 322282 sequences. (Running on oeis4.)