%I #11 May 13 2023 15:35:44
%S 1,115,645,1911,4233,7931,13325,20735,30481,42883,58261,76935,99225,
%T 125451,155933,190991,230945,276115,326821,383383,446121,515355,
%U 591405,674591,765233,863651,970165,1085095,1208761,1341483,1483581,1635375,1797185,1969331
%N Odd heptagonal pyramidal numbers.
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4, -6, 4, -1).
%F a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4).
%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) + 320.
%F a(n) = (2*n-1)*(4*n-3)*(20*n-17)/3.
%F G.f.: x*(1 + 111*x + 191*x^2 + 17*x^3)/(1-x)^4.
%e The sequence of heptagonal pyramidal numbers A002413 begins 1, 8, 26, 60, 115, 196, 308, 456, 645, 880, ... . As the third odd term is 645, a(3) = 645.
%t LinearRecurrence[{4,-6,4,-1},{1,115,645,1911},34]
%Y Cf. A002413, A218325.
%K nonn,easy
%O 1,2
%A _Ant King_, Oct 26 2012
|