A176889 a(2*k-1)=1, a(2*k)=2*k^2 (definition by T. M. Apostol, see References).

1, 2, 1, 8, 1, 18, 1, 32, 1, 50, 1, 72, 1, 98, 1, 128, 1, 162, 1, 200, 1, 242, 1, 288, 1, 338, 1, 392, 1, 450, 1, 512, 1, 578, 1, 648, 1, 722, 1, 800, 1, 882, 1, 968, 1, 1058, 1, 1152, 1, 1250, 1, 1352, 1, 1458, 1, 1568, 1, 1682, 1, 1800, 1, 1922, 1, 2048, 1, 2178

Offset

1,2

References

T. M. Apostol, Calculus, Volume 1, John Wiley & Sons, 1967 (2nd ed.), p. 378-379.

Links

Bruno Berselli, Table of n, a(n) for n = 1..5000

Index entries for linear recurrences with constant coefficients, signature (0,3,0,-3,0,1).

Formula

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

a(n) = a(-n) = 1+((-1)^n+1)*(n^2-2)/4.

Mathematica

CoefficientList[Series[(1 + 2 x - 2 x^2 + 2 x^3 + x^4) / (1 - x^2)^3, {x, 0, 65}], x] (* Vincenzo Librandi, Aug 19 2013 *)

Prog

(Magma) &cat[[1, 2*n^2]: n in [1..33]];
(Magma) [1+((-1)^n+1)*(n^2-2)/4: n in [1..70]]; // Vincenzo Librandi, Aug 19 2013

Crossrefs

Sequence in context: A125911 A009385 A008308 * A208753 A118931 A101280

Adjacent sequences: A176886 A176887 A176888 * A176890 A176891 A176892

Keyword

nonn,easy

Author

Bruno Berselli, Jan 11 2011

Status

approved