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A055430 Number of points in Z^n of norm <= 6.

%I A055430 #21 Jul 05 2024 14:08:35
%S A055430 1,13,113,925,6577,42205,252673,1405325,7259297,35372141,164379601,
%T A055430 733618493,3146718929,12990499005,51718535393,198914813101,
%U A055430 740760081985,2678069599181,9420136888369,32289213758941
%N A055430 Number of points in Z^n of norm <= 6.
%H A055430 Andrew Howroyd, <a href="/A055430/b055430.txt">Table of n, a(n) for n = 0..1000</a>
%H A055430 <a href="/index/Rec#order_37">Index entries for linear recurrences with constant coefficients</a>, signature (37, -666, 7770, -66045, 435897, -2324784, 10295472, -38608020, 124403620, -348330136, 854992152, -1852482996, 3562467300, -6107086800, 9364199760, -12875774670, 15905368710, -17672631900, 17672631900, -15905368710, 12875774670, -9364199760, 6107086800, -3562467300, 1852482996, -854992152, 348330136, -124403620, 38608020, -10295472, 2324784, -435897, 66045, -7770, 666, -37, 1).
%F A055430 From _Chai Wah Wu_, Jun 24 2024: (Start)
%F A055430 a(n) = 37*a(n-1) - 666*a(n-2) + 7770*a(n-3) - 66045*a(n-4) + 435897*a(n-5) - 2324784*a(n-6) + 10295472*a(n-7) - 38608020*a(n-8) + 124403620*a(n-9) - 348330136*a(n-10) + 854992152*a(n-11) - 1852482996*a(n-12) + 3562467300*a(n-13) - 6107086800*a(n-14) + 9364199760*a(n-15) - 12875774670*a(n-16) + 15905368710*a(n-17) - 17672631900*a(n-18) + 17672631900*a(n-19) - 15905368710*a(n-20) + 12875774670*a(n-21) - 9364199760*a(n-22) + 6107086800*a(n-23) - 3562467300*a(n-24) + 1852482996*a(n-25) - 854992152*a(n-26) + 348330136*a(n-27) - 124403620*a(n-28) + 38608020*a(n-29) - 10295472*a(n-30) + 2324784*a(n-31) - 435897*a(n-32) + 66045*a(n-33) - 7770*a(n-34) + 666*a(n-35) - 37*a(n-36) + a(n-37) for n > 36.
%F A055430 G.f.: (-281965*x^36 - 162444640*x^35 - 11761370826*x^34 - 212144886152*x^33 - 928459493209*x^32 + 1366727925344*x^31 + 5450543439600*x^30 - 13901610703968*x^29 + 5010411747228*x^28 + 24002105533408*x^27 - 48129204006968*x^26 + 44288625555072*x^25 - 17538634969732*x^24 - 9564481773600*x^23 + 21935655852496*x^22 - 20357294743904*x^21 + 13092000949610*x^20 - 6522919407712*x^19 + 2638636104868*x^18 - 890508942928*x^17 + 255606629458*x^16 - 63337866464*x^15 + 13802270992*x^14 - 2818810912*x^13 + 658326476*x^12 - 212266848*x^11 + 77735560*x^10 - 24527552*x^9 + 5749644*x^8 - 823648*x^7 - 5328*x^6 + 40416*x^5 - 12645*x^4 + 2368*x^3 - 298*x^2 + 24*x - 1)/(x - 1)^37. (End)
%t A055430 a[n_] := SeriesCoefficient[1/(1-x) Sum[x^(i^2), {i, -6, 6}]^n, {x, 0, 36}];
%t A055430 a /@ Range[0, 19] (* _Jean-François Alcover_, Sep 29 2019, from A302997 *)
%Y A055430 Row n=6 of A302997.
%K A055430 nonn,easy
%O A055430 0,2
%A A055430 _David W. Wilson_