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%I #5 Jun 13 2015 00:55:37
%S 946,1540,13695,1151403,18773128,1590903028,25941294753,2198372138061,
%T 20904988593016,35846699817610,340877159895525,28887334308843153,
%U 471037447946228878,39917653136343078778,650898046192856866503,55159780922590010984691
%N Hexagonal numbers (A000384) that are the sum of eleven consecutive hexagonal numbers.
%H Colin Barker, <a href="/A257722/b257722.txt">Table of n, a(n) for n = 1..767</a>
%H <a href="/index/Rec#order_17">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,0,0,25091193602,-25091193602,0,0,0,0,0,0,-1,1).
%F G.f.: -11*x*(21*x^16 +252*x^15 +4025*x^14 +359100*x^13 +5562025*x^12 +496218492*x^11 +4272895055*x^10 +3412929546*x^9 -457241153867*x^8 +197493713028*x^7 +2213671975*x^6 +142920900*x^5 +1601975*x^4 +103428*x^3 +1105*x^2 +54*x +86) / ((x -1)*(x^2 -20*x +1)*(x^2 +20*x +1)*(x^4 +398*x^2 +1)*(x^8 +158402*x^4 +1)).
%e 946 is in the sequence because H(22) = 946 = 1 + 6 + 15 + 28 + 45 + 66 + 91 + 120 + 153 + 190 + 231 = H(1)+...+H(11).
%o (PARI) Vec(-11*x*(21*x^16 +252*x^15 +4025*x^14 +359100*x^13 +5562025*x^12 +496218492*x^11 +4272895055*x^10 +3412929546*x^9 -457241153867*x^8 +197493713028*x^7 +2213671975*x^6 +142920900*x^5 +1601975*x^4 +103428*x^3 +1105*x^2 +54*x +86) / ((x -1)*(x^2 -20*x +1)*(x^2 +20*x +1)*(x^4 +398*x^2 +1)*(x^8 +158402*x^4 +1)) + O(x^100))
%Y Cf. A257721, A257723, A257724.
%K nonn,easy
%O 1,1
%A _Colin Barker_, May 06 2015
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