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A103831 For even n, a(n) = n*(n+1), for odd n, a(n) = 2*n + 1. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
First the product then the sum of two successive integers.
LINKS
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
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

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Last modified March 29 09:59 EDT 2024. Contains 371268 sequences. (Running on oeis4.)