A103831 For even n, a(n) = n*(n+1), for odd n, a(n) = 2*n + 1.

0, 3, 6, 7, 20, 11, 42, 15, 72, 19, 110, 23, 156, 27, 210, 31, 272, 35, 342, 39, 420, 43, 506, 47, 600, 51, 702, 55, 812, 59, 930, 63, 1056, 67, 1190, 71, 1332, 75, 1482, 79, 1640, 83, 1806, 87, 1980, 91, 2162, 95, 2352, 99, 2550, 103, 2756, 107, 2970, 111, 3192, 115

Offset

0,2

Comments

First the product then the sum 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.: (6*x^5+3*x^4-18*x^3-10*x^2+20*x+7) / (1-x)^3*(1+x)^3.

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

E.g.f.: (x^2 + 2*x)*cosh(x) + (2*x + 1)*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=20, a(5)=5+6=11.

Mathematica

Flatten[Table[{i + i + 1, (i + 1)(i + 2)}, {i, 1, 99, 2}]]

Prog

(Python)
for n in range(0, 10**3):
    print((n**2+3*n+1+(n**2-n-1)*(-1)**n)/2)
# Soumil Mandal, Apr 14 2016
(Magma) [IsOdd(n) select (2*n+1) else n*(n+1): n in [0..52]]; // Vincenzo Librandi, Apr 14 2016

Crossrefs

Cf. A103832.

Sequence in context: A259256 A056703 A113534 * A217519 A364007 A106357

Adjacent sequences: A103828 A103829 A103830 * A103832 A103833 A103834

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

Status

approved