A103832 For even n, a(n)=2n+1, for odd n, a(n)=n(n+1)

1, 2, 5, 12, 9, 30, 13, 56, 17, 90, 21, 132, 25, 182, 29, 240, 33, 306, 37, 380, 41, 462, 45, 552, 49, 650, 53, 756, 57, 870, 61, 992, 65, 1122, 69, 1260, 73, 1406, 77, 1560, 81, 1722, 85, 1892, 89, 2070, 93, 2256, 97, 2450, 101, 2652, 105, 2862, 109, 3080, 113

Offset

0,2

Comments

First the sum then the product of two successive integers.

Links

G. C. Greubel, Table of n, a(n) for n = 0..5000

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

Formula

G.f.: (1+3x^2)(1+2x-x^2)/((1-x)^3*(1+x)^3). [R. J. Mathar, Aug 30 2008]

a(n) = (n^2+3*n+1-(n^2-n-1)*(-1)^n)/2. - Luce ETIENNE, Apr 13 2016

E.g.f.: (2*x+1)*cosh(x) + (x^2 + 2*x)*sinh(x). - Ilya Gutkovskiy, Apr 13 2016

a(n) = 3*a(n-2) - 3*a(n-4) + a(n-6). - G. C. Greubel, Apr 13 2016

Example

a(4)=4+5=9, a(5)=5*6=30.

Maple

seq(2*n+1+(n mod 2)*(n^2-n-1), n=0..100); # Robert Israel, Apr 14 2016

Mathematica

Flatten[Table[{i + i + 1, (i + 1)(i + 2)}, {i, 0, 98, 2}]]
LinearRecurrence[{0, 3, 0, -3, 0, 1}, {1, 2, 5, 12, 9, 30}, 60] (* Harvey P. Dale, Oct 07 2016 *)

Prog

(Python)
for n in range(0, 10**3):
    print((int)((n**2+3*n+1-(n**2-n-1)*(-1)**n)/2))
# Soumil Mandal, Apr 14 2016

Crossrefs

Cf. A103831.

Sequence in context: A110020 A070266 A125199 * A348891 A191368 A085227

Adjacent sequences: A103829 A103830 A103831 * A103833 A103834 A103835

Keyword

nonn

Author

Zak Seidov, Feb 17 2005, Feb 18 2005

Extensions

Edited by N. J. A. Sloane, Aug 29 2008 at the suggestion of R. J. Mathar

Corrected typo in the definition - R. J. Mathar, Sep 07 2010

Status

approved