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A014632
Odd pentagonal numbers.
5
1, 5, 35, 51, 117, 145, 247, 287, 425, 477, 651, 715, 925, 1001, 1247, 1335, 1617, 1717, 2035, 2147, 2501, 2625, 3015, 3151, 3577, 3725, 4187, 4347, 4845, 5017, 5551, 5735, 6305, 6501, 7107, 7315, 7957, 8177, 8855, 9087, 9801, 10045, 10795, 11051, 11837
OFFSET
0,2
FORMULA
a(n) = a(n-1) +2*a(n-2) -2*a(n-3) -a(n-4) +a(n-5).
a(n) = 48+2*a(n-2)-a(n-4). - Ant King, Aug 16 2011
G.f.: (1+4*x+28*x^2+8*x^3+7*x^4)/((1+x)^2*(1-x)^3). - R. J. Mathar, Jul 25 2009
a(n) = (3*(-1)^n+12*n+1)*((-1)^n+4*n+1)/8. - Ant King, Aug 16 2011
Sum_{n>=0} 1/a(n) = Pi/4 + 3*log(3)/2 + sqrt(3)*log(2-sqrt(3))/2. - Amiram Eldar, Jan 13 2024
MAPLE
A014632:=n->(3*(-1)^n+12*n+1)*((-1)^n+4*n+1)/8: seq(A014632(n), n=0..100); # Wesley Ivan Hurt, Apr 28 2017
MATHEMATICA
Select[Table[n (3 n - 1)/2, {n, 100}], OddQ] (* Harvey P. Dale, Feb 03 2011 *)
PROG
(Magma) [1/8*(11+3*(-1)^(n+1)-12*(n+1))*(3+(-1)^(n+1)-4*(n+1)): n in [0..40]]; // Vincenzo Librandi, Aug 17 2011
CROSSREFS
Sequence in context: A376610 A128044 A299529 * A117985 A371561 A115707
KEYWORD
nonn,easy
EXTENSIONS
More terms from Patrick De Geest
STATUS
approved