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A085473
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a(n) = 6*n^2 + 3*n + 1.
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8
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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
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OFFSET
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0,2
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COMMENTS
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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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LINKS
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FORMULA
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G.f.: (1 + 7*x + 4*x^2)/(1 - x)^3.
a(n) = binomial(2*n+3,3) - binomial(2*n,3).
a(0)=1, a(1)=10, a(2)=31; for n>2, a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Harvey P. Dale, Nov 15 2011
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MATHEMATICA
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Table[Binomial[2 n + 3, 3] - Binomial[2 n, 3], {n, 0, 50}] (* or *) LinearRecurrence[{3, -3, 1}, {1, 10, 31}, 50] (* Harvey P. Dale, Nov 15 2011 *)
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PROG
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(PARI) x='x+O('x^50); Vec((1+7x+4x^2)/(1-x)^3) \\ G. C. Greubel, Jun 13 2017
(PARI) for(n=0, 25, print1(6*n^2 + 3*n + 1, ", ")) \\ G. C. Greubel, Jun 13 2017
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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