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A218330 Odd decagonal pyramidal numbers. 1

%I #7 Aug 01 2015 10:38:44

%S 1,11,175,301,1005,1375,3003,3745,6681,7923,12551,14421,21125,23751,

%T 32915,36425,48433,52955,68191,73853,92701,99631,122475,130801,158025,

%U 167875,199863,211365,248501,261783,304451,319641,368225,385451,440335,459725,521293

%N Odd 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-17)*(4*n-(-1)^n-3)*(4*n-(-1)^n-1)/24.

%F G. f. x*(1+10*x+161*x^2+96*x^3+215*x^4+22*x^5+7*x^6)/((1-x)^4*(1+x)^3).

%e The sequence of decagonal pyramidal numbers A007585 begins 0, 1, 11, 38, 90, 175, 301, 476, 708, 1005, 1375,... As the third odd term is 175, then a(3) = 175.

%t LinearRecurrence[{1,3,-3,-3,3,1,-1}, {1,11,175,301,1005,1375,3003}, 37]

%Y Cf. A007585, A218331.

%K nonn

%O 1,2

%A _Ant King_, Oct 29 2012

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