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

Author

Mohammad K. Azarian

Keywords

• nonn
• easy

Links

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

Crossrefs

Cf. A000566, A014640, A014773, A014792.

Programs

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 *)

PARI

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

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)

Extensions

Extended and description corrected by Patrick De Geest