A110349 a(n) = n + (n+1) + (n-1) + (n+2) + (n-2) ... n terms.

1, 5, 9, 18, 25, 39, 49, 68, 81, 105, 121, 150, 169, 203, 225, 264, 289, 333, 361, 410, 441, 495, 529, 588, 625, 689, 729, 798, 841, 915, 961, 1040, 1089, 1173, 1225, 1314, 1369, 1463, 1521, 1620, 1681, 1785, 1849, 1958, 2025, 2139, 2209, 2328, 2401, 2525

Offset

1,2

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Robert M. Ziff, On Cardy's formula for the critical crossing probability in 2d percolation, J. Phys. A. 28, 1249-1255 (1995).

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

Formula

a(2n-1) = (2n-1)^2; a(2n)=4n^2+n. - Emeric Deutsch, Aug 03 2005

G.f.: x*(1+4*x+2*x^2+x^3)/((1+x)^2*(1-x)^3). - Bruno Berselli, Mar 19 2012

a(n) = n(4n+(-1)^n+1)/4. - Bruno Berselli, Mar 19 2012

Example

a(4) = 4+5+3+6 = 18.
a(5) = 5+6+4+7+3 = 25.

Maple

a:=proc(n) if n mod 2 = 0 then n^2+n/2 else n^2 fi end: seq(a(n), n=1..60); # Emeric Deutsch, Aug 03 2005

Mathematica

f[n_]:=If[OddQ[n], n^2, n/2*(2n+1)]; Array[f, 50] (* Harvey P. Dale, Mar 17 2012 *)

Crossrefs

Sequence in context: A315119 A372709 A061502 * A036832 A257595 A116453

Adjacent sequences: A110346 A110347 A110348 * A110350 A110351 A110352

Keyword

nonn,easy

Author

Amarnath Murthy, Jul 21 2005

Extensions

More terms from Emeric Deutsch, Aug 03 2005

Status

approved