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A055429 Number of points in Z^n of norm <= 5. 2

%I #23 Jul 05 2024 14:07:58

%S 1,11,81,515,3121,16875,84769,394691,1733537,7129227,27634481,

%T 102386243,365127249,1256538091,4180101249,13457728387,41966634049,

%U 126929576971,373074639633,1067860637059,2981845163377,8133266915563

%N Number of points in Z^n of norm <= 5.

%H Andrew Howroyd, <a href="/A055429/b055429.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_26">Index entries for linear recurrences with constant coefficients</a>, signature (26, -325, 2600, -14950, 65780, -230230, 657800, -1562275, 3124550, -5311735, 7726160, -9657700, 10400600, -9657700, 7726160, -5311735, 3124550, -1562275, 657800, -230230, 65780, -14950, 2600, -325, 26, -1).

%F From _Chai Wah Wu_, Jun 24 2024: (Start)

%F a(n) = 26*a(n-1) - 325*a(n-2) + 2600*a(n-3) - 14950*a(n-4) + 65780*a(n-5) - 230230*a(n-6) + 657800*a(n-7) - 1562275*a(n-8) + 3124550*a(n-9) - 5311735*a(n-10) + 7726160*a(n-11) - 9657700*a(n-12) + 10400600*a(n-13) - 9657700*a(n-14) + 7726160*a(n-15) - 5311735*a(n-16) + 3124550*a(n-17) - 1562275*a(n-18) + 657800*a(n-19) - 230230*a(n-20) + 65780*a(n-21) - 14950*a(n-22) + 2600*a(n-23) - 325*a(n-24) + 26*a(n-25) - a(n-26) for n > 25.

%F G.f.: (17661*x^25 + 2780045*x^24 + 57398752*x^23 + 196406336*x^22 - 384767594*x^21 - 344776842*x^20 + 1472178776*x^19 - 1618643528*x^18 + 654551287*x^17 + 375150567*x^16 - 758544352*x^15 + 613843168*x^14 - 335122748*x^13 + 139534596*x^12 - 47458608*x^11 + 14003344*x^10 - 3738565*x^9 + 903851*x^8 - 193728*x^7 + 38944*x^6 - 8826*x^5 + 2406*x^4 - 616*x^3 + 120*x^2 - 15*x + 1)/(x - 1)^26. (End)

%t a[n_] := SeriesCoefficient[1/(1-x) Sum[x^(i^2), {i, -5, 5}]^n, {x, 0, 25}];

%t a /@ Range[0, 21] (* _Jean-Fran├žois Alcover_, Sep 29 2019, from A302997 *)

%Y Row n=5 of A302997.

%K nonn,easy

%O 0,2

%A _David W. Wilson_

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Last modified July 22 22:22 EDT 2024. Contains 374544 sequences. (Running on oeis4.)