A351353 - OEIS

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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

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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 A377587 A355696

Adjacent sequences: A351350 A351351 A351352 * A351354 A351355 A351356

KEYWORD

nonn,easy

AUTHOR

Lamine Ngom, Feb 08 2022

STATUS

approved