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Squares of even heptagonal numbers.
5

%I #19 Oct 06 2019 17:27:35

%S 0,324,1156,12544,21904,81796,116964,291600,379456,763876,940900,

%T 1658944,1971216,3175524,3678724,5550736,6310144,9060100,10150596,

%U 14017536,15523600,20775364,22791076,29724304,32353344,41293476,44649124,55950400,60155536,74200996

%N Squares of even heptagonal numbers.

%H Colin Barker, <a href="/A014792/b014792.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (1,4,-4,-6,6,4,-4,-1,1).

%F From _Colin Barker_, Dec 17 2015: (Start)

%F a(n) = (1/2)*(200*n^4 - 120*n^3 + 18*n^2) for n even.

%F a(n) = (1/2)*(200*n^4 + 280*n^3 + 138*n^2 + 28*n + 2) for n odd.

%F G.f.: 4*x*(81 + 208*x + 2523*x^2 + 1508*x^3 + 4071*x^4 + 680*x^5 + 525*x^6 + 4*x^7) / ((1-x)^5*(1+x)^4).

%F (End)

%t Select[Table[(n(5n-3))/2,{n,0,60}],EvenQ]^2 (* _Harvey P. Dale_, Jul 24 2015 *)

%o (PARI) concat(0, Vec(4*x*(81+208*x+2523*x^2+1508*x^3+4071*x^4+680*x^5+525*x^6+4*x^7) / ((1-x)^5*(1+x)^4) + O(x^40))) \\ _Colin Barker_, Dec 17 2015

%Y Cf. A000566, A014637, A014640, A014773.

%K nonn,easy

%O 0,2

%A _Mohammad K. Azarian_

%E More terms from _Patrick De Geest_, Aug 17 2000