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A085473
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C(2n+3,3)-C(2n,3).
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4
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1, 10, 31, 64, 109, 166, 235, 316, 409, 514, 631, 760, 901, 1054, 1219, 1396, 1585, 1786, 1999, 2224, 2461, 2710, 2971, 3244, 3529, 3826, 4135, 4456, 4789, 5134, 5491, 5860, 6241, 6634, 7039, 7456, 7885, 8326, 8779, 9244, 9721, 10210, 10711, 11224
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| T(n,3) of A085475.
Sequence found by reading the line from 1, in the direction 1, 10,..., in the square spiral whose vertices are the generalized pentagonal numbers A001318. - Omar E. Pol, Sep 09 2011
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FORMULA
| G.f.: (1+7x+4x^2)/(1-x)^3; a(n)=6n^2+3n+1.
a(n)=12*n+a(n-1)-3 (with a(0)=1) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Aug 08 2010]
a(0)=1, a(1)=10, a(2)=31, a(n)=3*a(n-1)-3*a(n-2)+a(n-3) [From Harvey P. Dale, Nov 15 2011]
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EXAMPLE
| a(1)=12*1+1-3=10; a(2)=12*2+10-3=31; a(3)=12*3+31-3=64 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Aug 08 2010]
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MATHEMATICA
| Table[3*n*(2*n+1)+1, {n, 0, 100}] (* From Vladimir Joseph Stephan Orlovsky, Jul 06 2011 *)
Table[Binomial[2n+3, 3]-Binomial[2n, 3], {n, 0, 50}] (* or *) LinearRecurrence[ {3, -3, 1}, {1, 10, 31}, 50] (* From Harvey P. Dale, Nov 15 2011 *)
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CROSSREFS
| Cf. A016813, A085474.
Sequence in context: A187633 A063154 A100500 * A051943 A059306 A192023
Adjacent sequences: A085470 A085471 A085472 * A085474 A085475 A085476
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KEYWORD
| easy,nonn
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Jul 01 2003
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