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
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).
Programs
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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 *) -
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
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)
Extensions
Extended and description corrected by Patrick De Geest