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

1,2

Comments

All terms are Lucas numbers (A000032).

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

Links

Table of n, a(n) for n=1..25.

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

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

Cf. A195317, A007310, A000032.

Sequence in context: A122095 A282137 A027758 * A285992 A355696 A271348

Adjacent sequences: A351350 A351351 A351352 * A351354 A351355 A351356

Keyword

nonn,easy

Author

Lamine Ngom, Feb 08 2022

Status

approved