|
%I #30 Sep 14 2022 14:56:56
%S 1,7,55,81,189,235,403,469,697,783,1071,1177,1525,1651,2059,2205,2673,
%T 2839,3367,3553,4141,4347,4995,5221,5929,6175,6943,7209,8037,8323,
%U 9211,9517,10465,10791,11799,12145,13213,13579,14707,15093,16281,16687,17935
%N Odd heptagonal numbers (A000566).
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,2,-2,-1,1).
%F 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]
%F From _Ant King_, Sep 01 2011: (Start)
%F a(n) = (1/8)*(1+(-1)^n+4*n)*(-1+5*(-1)^n+20*n)
%F a(n) = a(n-1)+2*a(n-2)-2*a(n-3)-a(n-4)+a(n-5)
%F a(n) = 80+2*a(n-2)-a(n-4)
%F (End)
%t Table[1/8 (1+(-1)^n+4 n) (-1+5 (-1)^n+20 n),{n,0,42}] (* _Ant King_, Sep 01 2011 *)
%t 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 *)
%o (PARI) a(n)=(5*(-1)^n+20*n-1)*(4*n+1+(-1)^n)/8 \\ _Charles R Greathouse IV_, Sep 01 2011
%Y Cf. A000566, A014640, A014773, A014792.
%K nonn,easy
%O 0,2
%A _Mohammad K. Azarian_
%E Extended and description corrected by _Patrick De Geest_
|
