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17, 65, 145, 257, 401, 577, 785, 1025, 1297, 1601, 1937, 2305, 2705, 3137, 3601, 4097, 4625, 5185, 5777, 6401, 7057, 7745, 8465, 9217, 10001, 10817, 11665, 12545, 13457, 14401, 15377, 16385, 17425, 18497, 19601, 20737, 21905, 23105, 24337, 25601
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Area of a Maltese cross conventionally inscribed in a 5n X 5n-grid.
Areas of some other crosses, each made from unit squares, as shown in Weisstein's illustrations: Greek Cross = x-pentomino = 5. Latin Cross = 6. Saint Andrew's cross = crux decussata = 9. Saint Anthony's Cross = tau cross = crux commissa = 10. Gaullist Cross = cross of lorraine or patriarchal cross = 13. Papal Cross = 22. - Jonathan Vos Post, Jun 18 2005
The identity (16*n^2+1)^2-(64*n^2+8)*(2*n)^2 = 1 can be written as a(n)^2-A158488(n)*A005843(n)^2 = 1. - Vincenzo Librandi, Feb 08 2012
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Maltese Cross
Eric Weisstein's World of Mathematics, Gaullist Cross.
Eric Weisstein's World of Mathematics, Greek Cross.
Eric Weisstein's World of Mathematics, Latin Cross.
Index to sequences with linear recurrences with constant coefficients, signature (3,-3,1).
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FORMULA
| a(n) = A002522(4*n) = A016802(n) + 1.
G.f.: x*(17+14*x+x^2)/(1-x)^3. - Bruno Berselli, Feb 08 2012
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MATHEMATICA
| LinearRecurrence[{3, -3, 1}, {17, 65, 145}, 40] (* Vincenzo Librandi, Feb 08 2012 *)
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PROG
| (PARI) a(n)= 16*n^2+1 \\ Charles R Greathouse IV, Dec 23 2011
(MAGMA) I:=[17, 65, 145]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+Self(n-3): n in [1..50]]; // Vincenzo Librandi, Feb 08 2012
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CROSSREFS
| Cf. A005843, A158488.
Sequence in context: A125992 A054402 A086533 * A130885 A036545 A146807
Adjacent sequences: A108208 A108209 A108210 * A108212 A108213 A108214
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KEYWORD
| nonn,easy,changed
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AUTHOR
| Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jun 15 2005
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