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Squares of odd heptagonal numbers.
5

%I #12 Dec 17 2015 09:43:12

%S 1,49,3025,6561,35721,55225,162409,219961,485809,613089,1147041,

%T 1385329,2325625,2725801,4239481,4862025,7144929,8059921,11336689,

%U 12623809,17147881,18896409,24950025,27258841,35153041,38130625,48205249,51969681,64593369,69272329

%N Squares of odd heptagonal numbers.

%H Colin Barker, <a href="/A014773/b014773.txt">Table of n, a(n) for n = 1..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^4-920*n^3+1578*n^2-1196*n+338) for n even.

%F a(n) = 1/2*(200*n^4-520*n^3+498*n^2-208*n+32) for n odd.

%F G.f.: x*(1+48*x+2972*x^2+3344*x^3+17262*x^4+5648*x^5+8396*x^6+560*x^7+169*x^8) / ((1-x)^5*(1+x)^4).

%F (End)

%t Table[SeriesCoefficient[x (1 + 48 x + 2972 x^2 + 3344 x^3 + 17262 x^4 + 5648 x^5 + 8396 x^6 + 560 x^7 + 169 x^8)/((1 - x)^5 (1 + x)^4), {x, 0, n}], {n, 30}] (* _Michael De Vlieger_, Dec 17 2015 *)

%o (PARI) Vec(x*(1+48*x+2972*x^2+3344*x^3+17262*x^4+5648*x^5+8396*x^6+560*x^7+169*x^8) / ((1-x)^5*(1+x)^4) + O(x^40)) \\ _Colin Barker_, Dec 17 2015

%Y Cf. A000566, A014637, A014640, A014792.

%K nonn,easy

%O 1,2

%A _Mohammad K. Azarian_

%E More terms from _Erich Friedman_.