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%I #11 Oct 18 2022 15:27:13
%S 1,155,885,2639,5865,11011,18525,28855,42449,59755,81221,107295,
%T 138425,175059,217645,266631,322465,385595,456469,535535,623241,
%U 720035,826365,942679,1069425,1207051,1356005,1516735,1689689,1875315,2074061,2286375,2512705
%N Odd 9-gonal (nonagonal) 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) + 448.
%F a(n) = (2*n-1)*(4*n-3)*(28*n-25)/3.
%F G.f.: x*(1+151*x+271*x^2+25*x^3)/(1-x)^4.
%e The sequence of 9-gonal (nonagonal) pyramidal numbers A007584 begins 1, 10, 34, 80, 155, 266, 420, 624, 885, 1210, .... As the third odd term is 885, then a(3) = 885.
%t LinearRecurrence[{4,-6,4,-1},{1,155,885,2639},33]
%o (PARI) a(n)=(2*n-1)*(4*n-3)*(28*n-25)/3 \\ _Charles R Greathouse IV_, Oct 18 2022
%Y Cf. A007584, A218329.
%K nonn,easy
%O 1,2
%A _Ant King_, Oct 28 2012