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A140672
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n*(3*n + 13)/2.
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13
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0, 8, 19, 33, 50, 70, 93, 119, 148, 180, 215, 253, 294, 338, 385, 435, 488, 544, 603, 665, 730, 798, 869, 943, 1020, 1100, 1183, 1269, 1358, 1450, 1545, 1643, 1744, 1848, 1955, 2065, 2178, 2294, 2413, 2535, 2660, 2788, 2919, 3053
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OFFSET
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0,2
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LINKS
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Table of n, a(n) for n=0..43.
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FORMULA
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a(n)=(3*n^2 + 13*n)/2.
a(n)=3*n+a(n-1)+5 (with a(0)=0) [From Vincenzo Librandi, Aug 03 2010]
a(0)=0, a(1)=8, a(2)=19, a(n)=3*a(n-1)-3*a(n-2)+a(n-3) [From Harvey P. Dale, Dec 16 2011]
G.f.: x*(8 - 5*x)/(1 - x)^3. [Arkadiusz Wesolowski, Dec 24 2011]
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EXAMPLE
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a(1)=3*1+0+5=8; a(2)=3*2+8+5=19; a(3)=3*3+19+5=33 [From Vincenzo Librandi, Aug 03 2010]
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MAPLE
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with(finance):seq(add(cashflows([2, k, n], 0 ), k=3..n), n=2..45); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 22 2008
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MATHEMATICA
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s=0; lst={s}; Do[s+=n++ +8; AppendTo[lst, s], {n, 0, 6!, 3}]; lst [From Vladimir Joseph Stephan Orlovsky, Nov 16 2008]
Table[n (3n+13)/2, {n, 0, 50}] (* or *) LinearRecurrence[{3, -3, 1}, {0, 8, 19}, 50] (* From Harvey P. Dale, Dec 16 2011 *)
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CROSSREFS
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Cf. A000326, A005449, A045943, A115067, A140090, A140091, A059845, A140673, A140674, A140675.
The generalized pentagonal numbers b*n+3*n*(n-1)/2, for b = 1 through 12, form sequences A000326, A005449, A045943, A115067, A140090, A140091, A059845, A140672, A140673, A140674, A140675, A151542.
Sequence in context: A017485 A146270 A146222 * A135027 A158916 A045557
Adjacent sequences: A140669 A140670 A140671 * A140673 A140674 A140675
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KEYWORD
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easy,nonn
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AUTHOR
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Omar E. Pol, May 22 2008
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STATUS
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approved
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