A014640 Even heptagonal numbers (A000566).

0, 18, 34, 112, 148, 286, 342, 540, 616, 874, 970, 1288, 1404, 1782, 1918, 2356, 2512, 3010, 3186, 3744, 3940, 4558, 4774, 5452, 5688, 6426, 6682, 7480, 7756, 8614, 8910, 9828, 10144, 11122, 11458, 12496, 12852, 13950, 14326, 15484, 15880, 17098, 17514, 18792

Offset

0,2

Links

Colin Barker, Table of n, a(n) for n = 0..1000

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

Formula

G.f.: -2*x*(2*x^3+21*x^2+8*x+9) / ((x+1)^2*(x-1)^3) [From Maksym Voznyy (voznyy(AT)mail.ru), Aug 11 2009]

a(0)=0, a(1)=18, a(2)=34, a(3)=112, a(4)=148, a(n) = a(n-1)+2*a(n-2)-2*a(n-3)-a(n-4)+a(n-5). - Harvey P. Dale, Jun 16 2014

From Colin Barker, Jan 27 2016: (Start)

a(n) = (20*n^2-10*(-1)^n*n+4*n-(-1)^n+1)/2.

a(n) = 10*n^2-3*n for n even.

a(n) = 10*n^2+7*n+1 for n odd.

(End)

Mathematica

Select[Table[(n(5n-3))/2, {n, 0, 100}], EvenQ] (* or *) LinearRecurrence[ {1, 2, -2, -1, 1}, {0, 18, 34, 112, 148}, 50] (* Harvey P. Dale, Jun 16 2014 *)

Prog

(PARI) concat(0, Vec(2*x*(9+8*x+21*x^2+2*x^3)/((1-x)^3*(1+x)^2) + O(x^100))) \\ Colin Barker, Jan 27 2016

Crossrefs

Cf. A000566, A014637, A014773, A014792.

Sequence in context: A044063 A044444 A250770 * A238240 A245587 A215137

Adjacent sequences: A014637 A014638 A014639 * A014641 A014642 A014643

Keyword

nonn,easy

Author

Mohammad K. Azarian

Extensions

Extended and description corrected by Patrick De Geest

Status

approved