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A055431 Number of points in Z^n of norm <= 7. 2
1, 15, 149, 1419, 11833, 89527, 622573, 4031123, 24499121, 140246303, 759891589, 3936654683, 19595418729, 94005744199, 435555727453, 1952358697443, 8479351841889, 35738244759855, 146442095372661, 584453833956395 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
Index entries for linear recurrences with constant coefficients, signature (50, -1225, 19600, -230300, 2118760, -15890700, 99884400, -536878650, 2505433700, -10272278170, 37353738800, -121399651100, 354860518600, -937845656300, 2250829575120, -4923689695575, 9847379391150, -18053528883775, 30405943383200, -47129212243960, 67327446062800, -88749815264600, 108043253365600, -121548660036300, 126410606437752, -121548660036300, 108043253365600, -88749815264600, 67327446062800, -47129212243960, 30405943383200, -18053528883775, 9847379391150, -4923689695575, 2250829575120, -937845656300, 354860518600, -121399651100, 37353738800, -10272278170, 2505433700, -536878650, 99884400, -15890700, 2118760, -230300, 19600, -1225, 50, -1).
FORMULA
From Chai Wah Wu, Jun 24 2024: (Start)
a(n) = 50*a(n-1) - 1225*a(n-2) + 19600*a(n-3) - 230300*a(n-4) + 2118760*a(n-5) - 15890700*a(n-6) + 99884400*a(n-7) - 536878650*a(n-8) + 2505433700*a(n-9) - 10272278170*a(n-10) + 37353738800*a(n-11) - 121399651100*a(n-12) + 354860518600*a(n-13) - 937845656300*a(n-14) + 2250829575120*a(n-15) - 4923689695575*a(n-16) + 9847379391150*a(n-17) - 18053528883775*a(n-18) + 30405943383200*a(n-19) - 47129212243960*a(n-20) + 67327446062800*a(n-21) - 88749815264600*a(n-22) + 108043253365600*a(n-23) - 121548660036300*a(n-24) + 126410606437752*a(n-25) - 121548660036300*a(n-26) + 108043253365600*a(n-27) - 88749815264600*a(n-28) + 67327446062800*a(n-29) - 47129212243960*a(n-30) + 30405943383200*a(n-31) - 18053528883775*a(n-32) + 9847379391150*a(n-33) - 4923689695575*a(n-34) + 2250829575120*a(n-35) - 937845656300*a(n-36) + 354860518600*a(n-37) - 121399651100*a(n-38) + 37353738800*a(n-39) - 10272278170*a(n-40) + 2505433700*a(n-41) - 536878650*a(n-42) + 99884400*a(n-43) - 15890700*a(n-44) + 2118760*a(n-45) - 230300*a(n-46) + 19600*a(n-47) - 1225*a(n-48) + 50*a(n-49) - a(n-50) for n > 49.
G.f.: (4767165*x^49 + 9677003929*x^48 + 2099328748968*x^47 + 119350380239392*x^46 + 2336719571000548*x^45 + 15324790943793868*x^44 + 3669334003469912*x^43 - 165626545771418640*x^42 + 113225352874515162*x^41 + 773012391447229738*x^40 - 1795431077729032904*x^39 + 730347243679248128*x^38 + 3231774434773792276*x^37 - 7249751867677049972*x^36 + 7289414576709914312*x^35 - 2539411927923481168*x^34 - 3778300058198325229*x^33 + 7735724342915171551*x^32 - 7916127405687211504*x^31 + 5585783179325618368*x^30 - 2805508704881709112*x^29 + 850333720624628056*x^28 + 70648743414492144*x^27 - 307395947231217952*x^26 + 255873188698001516*x^25 - 149186455600233620*x^24 + 70664753999062000*x^23 - 28617884750559104*x^22 + 10133301697903944*x^21 - 3168161807821640*x^20 + 878763873242640*x^19 - 217944520543264*x^18 + 49563849545395*x^17 - 11011796480281*x^16 + 2633696463048*x^15 - 709532404192*x^14 + 200891132244*x^13 - 53924504996*x^12 + 12812092728*x^11 - 2574294736*x^10 + 411639898*x^9 - 44187894*x^8 + 222808*x^7 + 1253248*x^6 - 348508*x^5 + 59708*x^4 - 7256*x^3 + 624*x^2 - 35*x + 1)/(x - 1)^50. (End)
MATHEMATICA
a[n_] := SeriesCoefficient[1/(1-x) Sum[x^(i^2), {i, -7, 7}]^n, {x, 0, 49}];
a /@ Range[0, 19] (* Jean-François Alcover, Sep 29 2019, from A302997 *)
CROSSREFS
Row n=7 of A302997.
Sequence in context: A051272 A021414 A211847 * A119998 A119511 A023069
KEYWORD
nonn
AUTHOR
STATUS
approved

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Last modified July 13 17:35 EDT 2024. Contains 374284 sequences. (Running on oeis4.)