A243006 G.f.: (x - 3*x^2 + 12*x^3 + 6*x^4 - x^5) / ((1 - x) * (1 + x^2))^2.

0, 1, -1, 7, 27, 25, 2, 13, 54, 49, 5, 19, 81, 73, 8, 25, 108, 97, 11, 31, 135, 121, 14, 37, 162, 145, 17, 43, 189, 169, 20, 49, 216, 193, 23, 55, 243, 217, 26, 61, 270, 241, 29, 67, 297, 265, 32, 73, 324, 289, 35, 79, 351, 313, 38, 85, 378, 337, 41, 91, 405

Offset

0,4

Links

G. C. Greubel, Table of n, a(n) for n = 0..2500

Index entries for linear recurrences with constant coefficients, signature (2,-3,4,-3,2,-1)

Formula

a(4*n) = 27*n, a(4*n + 1) = 24*n + 1, a(4*n + 2) = 3*n - 1, a(4*n - 1) = 6*n + 1.

0 = a(n)*(+a(n+1) + 2*a(n+2) - a(n+3)) + a(n+1)*(-2*a(n+1) + 3*a(n+2) + 2*a(n+3)) + a(n+2)*(-2*a(n+2) + a(n+3)) for all n in Z.

Example

G.f. = x - x^2 + 7*x^3 + 27*x^4 + 25*x^5 + 2*x^6 + 13*x^7 + 54*x^8 + ...

Mathematica

CoefficientList[Series[(x-3*x^2+12*x^3+6*x^4-x^5)/((1-x)*(1+x^2))^2, {x, 0, 60}], x]  (* G. C. Greubel, Aug 06 2018 *)

Prog

(PARI) {a(n) = my(m = n\4); [27*m, 24*m + 1, 3*m - 1, 6*m + 7][n%4 + 1]};
(PARI) {a(n) = polcoeff( if( n<0, (x - 6*x^2 - 12*x^3 + 3*x^4 - x^5), (x - 3*x^2 + 12*x^3 + 6*x^4 - x^5)) / ((1 - x) * (1 + x^2))^2 + x * O(x^abs(n)), abs(n))};
(Magma) m:=60; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((x-3*x^2+12*x^3+6*x^4-x^5)/((1-x)*(1+x^2))^2)); // G. C. Greubel, Aug 06 2018

Crossrefs

Sequence in context: A183329 A342930 A166406 * A175377 A323113 A205861

Adjacent sequences: A243003 A243004 A243005 * A243007 A243008 A243009

Keyword

sign,easy

Author

Michael Somos, Aug 17 2014

Status

approved