A014637 Odd heptagonal numbers (A000566).

1, 7, 55, 81, 189, 235, 403, 469, 697, 783, 1071, 1177, 1525, 1651, 2059, 2205, 2673, 2839, 3367, 3553, 4141, 4347, 4995, 5221, 5929, 6175, 6943, 7209, 8037, 8323, 9211, 9517, 10465, 10791, 11799, 12145, 13213, 13579, 14707, 15093, 16281, 16687, 17935

Offset

0,2

Links

Table of n, a(n) for n=0..42.

Index entries for linear recurrences with constant coefficients, signature (1,2,-2,-1,1).

Formula

G.f.:(1+13*x^4+14*x^3+46*x^2+6*x)/((1+x)^2*(1-x)^3) [From Maksym Voznyy (voznyy(AT)mail.ru), Aug 11 2009]

From Ant King, Sep 01 2011: (Start)

a(n) = (1/8)*(1+(-1)^n+4*n)*(-1+5*(-1)^n+20*n)

a(n) = a(n-1)+2*a(n-2)-2*a(n-3)-a(n-4)+a(n-5)

a(n) = 80+2*a(n-2)-a(n-4)

(End)

Mathematica

Table[1/8 (1+(-1)^n+4 n) (-1+5 (-1)^n+20 n), {n, 0, 42}] (* Ant King, Sep 01 2011 *)
Select[PolygonalNumber[7, Range[200]], OddQ] (* or *) LinearRecurrence[{1, 2, -2, -1, 1}, {1, 7, 55, 81, 189}, 50] (* Harvey P. Dale, Sep 14 2022 *)

Prog

(PARI) a(n)=(5*(-1)^n+20*n-1)*(4*n+1+(-1)^n)/8 \\ Charles R Greathouse IV, Sep 01 2011

Crossrefs

Cf. A000566, A014640, A014773, A014792.

Sequence in context: A203878 A043077 A192718 * A062212 A272864 A121183

Adjacent sequences: A014634 A014635 A014636 * A014638 A014639 A014640

Keyword

nonn,easy

Author

Mohammad K. Azarian

Extensions

Extended and description corrected by Patrick De Geest

Status

approved