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A351353
Numbers k such that k^2 is a centered 40-gonal number.
1
1, 11, 29, 199, 521, 3571, 9349, 64079, 167761, 1149851, 3010349, 20633239, 54018521, 370248451, 969323029, 6643838879, 17393796001, 119218851371, 312119004989, 2139295485799, 5600748293801, 38388099893011, 100501350283429, 688846502588399, 1803423556807921
OFFSET
1,2
COMMENTS
All terms are Lucas numbers (A000032).
Corresponding indices of centered 40-gonal numbers are listed in A351354.
FORMULA
a(n) = A000032(A007310(n)).
G.f.: x*(1 + 11*x + 11*x^2 + x^3)/((1 + 4*x - x^2)*(1 - 4*x - x^2)). - Stefano Spezia, Feb 12 2022
EXAMPLE
29 is in the sequence because 29^2 = 841 is a centered 40-gonal number (the 3rd centered 40-gonal number).
3571^2 = 12752041 is a centered 40-gonal number (the 799th centered 40-gonal number). Hence 3571 is in the sequence.
MAPLE
a[1] := 1: a[2] := 11: a[3] := 29: a[4] := 199: a[5] := 521:
for n from 6 to 25 do a[n] := a[n - 1] + 18*a[n - 2] - 18*a[n - 3] - a[n - 4] + a[n - 5]: od:
seq(a[n], n = 1 .. 25);
MATHEMATICA
LinearRecurrence[{0, 18, 0, -1}, {1, 11, 29, 199}, 25] (* Amiram Eldar, Feb 09 2022 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Lamine Ngom, Feb 08 2022
STATUS
approved