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15, 57, 127, 225, 351, 505, 687, 897, 1135, 1401, 1695, 2017, 2367, 2745, 3151, 3585, 4047, 4537, 5055, 5601, 6175, 6777, 7407, 8065, 8751, 9465, 10207, 10977, 11775, 12601, 13455, 14337, 15247, 16185, 17151, 18145, 19167, 20217, 21295, 22401
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| The identity (14*n^2+1)^2-(49*n^2+7)*(2*n)^2=1 can be written as a(n)^2-A158481(n)*A005843(n)^2=1.
Sequence found by reading the line from 15, in the direction 15, 57,..., in the square spiral whose vertices are the generalized enneagonal numbers numbers A118277. Also sequence found by reading the same line in the square spiral whose edges have length A195019 and whose vertices are the numbers A195020. - Omar E. Pol, Sep 13 2011
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 1..10000
Index to sequences with linear recurrences with constant coefficients, signature (3,-3,1).
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FORMULA
| a(n) = 3*a(n-1) -3*a(n-2) +a(n-3).
G.f: x*(15+12*x+x^2)/(1-x)^3.
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MATHEMATICA
| LinearRecurrence[{3, -3, 1}, {15, 57, 127}, 50]
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PROG
| (MAGMA) I:=[15, 57, 127]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..40]];
(PARI) a(n) = 14*n^2+1;
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CROSSREFS
| Cf. A005843, A158481.
Sequence in context: A043944 A140379 A020222 * A184223 A084815 A183942
Adjacent sequences: A158479 A158480 A158481 * A158483 A158484 A158485
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KEYWORD
| nonn,easy,changed
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AUTHOR
| Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 20 2009
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