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%I #21 Jul 30 2016 19:56:10
%S 22,50,252,372,946,1222,2360,2856,4750,5530,8372,9500,13482,15022,
%T 20336,22352,29190,31746,40300,43460,53922,57750,70312,74872,89726,
%U 95082,112420,118636,138650,145790,168672,176800,202742,211922,241116
%N Even hexagonal pyramidal numbers.
%H Ivan Panchenko, <a href="/A015226/b015226.txt">Table of n, a(n) for n = 0..1000</a>
%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 Even numbers of form n(n+1)(4n-1)/6.
%F Contribution from _Ant King_, Oct 25 2012: (Start)
%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) +256.
%F a(n) = (4*n+(-1)^n+5)*(4*n+(-1)^n+7)*(8*n+2*(-1)^n+9)/24.
%F G. f. 2*x*(11 + 14*x + 68*x^2 + 18*x^3 + 17*x^4) / ((1-x)^4*(1+x)^3).
%F (End)
%F E.g.f.: (1/6)*(3*(15 - 30*x + 8*x^2)*exp(-x) + (87 + 348*x + 228*x^2 + 32*x^3 ) *exp(x)). - _G. C. Greubel_, Jul 30 2016
%t Select[ Table[ n(n+1)(4n-1)/6, {n, 100} ], EvenQ ]
%t LinearRecurrence[{1,3,-3,-3,3,1,-1},{22,50,252,372,946,1222,2360},35] (* _Ant King_, Oct 25 2012 *)
%o (PARI) a(n)=(4*n+(-1)^n+5)*(4*n+(-1)^n+7)*(8*n+2*(-1)^n+9)/24 \\ _Charles R Greathouse IV_, Jul 30 2016
%K nonn,easy
%O 0,1
%A _Mohammad K. Azarian_, Dec 11 1999
%E More terms from _Erich Friedman_.
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