A014632 Odd pentagonal numbers.
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
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..10000
- Index entries for linear recurrences with constant coefficients, signature (1, 2, -2, -1, 1).
Programs
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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
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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
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Mathematica
Select[Table[n (3 n - 1)/2, {n,100}], OddQ] (* Harvey P. Dale, Feb 03 2011 *)
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
Extensions
More terms from Patrick De Geest