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

0,2

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).

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

Cf. A000326, A014633.

Sequence in context: A376610 A128044 A299529 * A117985 A371561 A115707

Adjacent sequences: A014629 A014630 A014631 * A014633 A014634 A014635

Keyword

nonn,easy

Author

Mohammad K. Azarian

Extensions

More terms from Patrick De Geest

Status

approved