A351353 Numbers k such that k^2 is a centered 40-gonal number.

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

Author

Lamine Ngom, Feb 08 2022

Keywords

• nonn
• easy
• changed

Comments

All terms are Lucas numbers (A000032).

Corresponding indices of centered 40-gonal numbers are listed in A351354.

Examples

			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.
		

Links

• Index entries for linear recurrences with constant coefficients, signature (0,18,0,-1).

Crossrefs

Cf. A195317, A007310, A000032.

Programs

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 *)

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

E.g.f.: exp(-2*x)*(exp(2*x) + (exp(4*x) - 2)*cosh(sqrt(5)*x) - sqrt(5)*sinh(sqrt(5)*x)). - Stefano Spezia, Sep 03 2025