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A081585
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Third row of Pascal-(1,3,1) array A081578.
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6
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1, 9, 33, 73, 129, 201, 289, 393, 513, 649, 801, 969, 1153, 1353, 1569, 1801, 2049, 2313, 2593, 2889, 3201, 3529, 3873, 4233, 4609, 5001, 5409, 5833, 6273, 6729, 7201, 7689, 8193, 8713, 9249, 9801, 10369, 10953, 11553, 12169, 12801, 13449, 14113
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| The identity (8*n^2+1)^2-(64*n^2+16)*n^2 = 1 can be written as a(n)^2-A157912(n)*n^2 = 1 for n>0. - Vincenzo Librandi, Feb 09 2012
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Index to sequences with linear recurrences with constant coefficients, signature (3,-3,1).
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FORMULA
| a(n)=1+8n^2. G.f.: (1+3x)^2/(1-x)^3.
a(n)=16*n+a(n-1)-8 (with a(0)=1) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Aug 08 2010]
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MATHEMATICA
| LinearRecurrence[{3, -3, 1}, {1, 9, 33}, 40] (* Vincenzo Librandi, Feb 09 2012 *)
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PROG
| (MAGMA) I:=[1, 9, 33]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..40]]; // Vincenzo Librandi, Feb 09 2012
(PARI) for(n=0, 50, print1(8*n^2+1", ")); \\ Vincenzo Librandi, Feb 09 2012
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CROSSREFS
| Cf. A016813, A081586, A157912.
Sequence in context: A092562 A103602 A205796 * A101990 A147170 A146823
Adjacent sequences: A081582 A081583 A081584 * A081586 A081587 A081588
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KEYWORD
| easy,nonn,changed
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Mar 23 2003
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