A218331 - OEIS

%I #10 Aug 11 2015 01:36:34

%S 38,90,476,708,1826,2366,4600,5576,9310,10850,16468,18700,26586,29638,

%T 40176,44176,57750,62826,79820,86100,106898,114510,139496,148568,

%U 178126,188786,223300,235676,275530,289750,335328,351520,403206,421498,479676,500196

%N Even, nonzero decagonal pyramidal numbers.

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (1,3,-3,-3,3,1,-1).

%F a(n) = a(n-1) + 3*a(n-2) - 3*a(n-3) - 3*a(n-4) + 3*a(n-5) + a(n-6) - a(n-7).

%F a(n) = 3*a(n-2) - 3*a(n-4) + a(n-6) + 512.

%F a(n) = (16*n-4*(-1)^n-1)*(4*n-(-1)^n+3)*(4*n-(-1)^n+1)/24.

%F G. f. 2*x*(19+26*x+136*x^2+38*x^3+37*x^4)/((1-x)^4*(1+x)^3).

%e The sequence of nonzero decagonal pyramidal numbers begins 1, 11, 38, 90, 175, 301, 476, 708, 1005, 1375,... As the third even term is 476, then a(3) = 476.

%t LinearRecurrence[{1,3,-3,-3,3,1,-1},{38,90,476,708,1826,2366,4600},36]

%Y Cf. A007585, A218330.

%K nonn,easy

%O 1,1

%A _Ant King_, Oct 29 2012