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A152734
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5 times pentagonal numbers: 5*n*(3*n-1)/2.
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13
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0, 5, 25, 60, 110, 175, 255, 350, 460, 585, 725, 880, 1050, 1235, 1435, 1650, 1880, 2125, 2385, 2660, 2950, 3255, 3575, 3910, 4260, 4625, 5005, 5400, 5810, 6235, 6675, 7130, 7600, 8085, 8585, 9100, 9630, 10175, 10735, 11310, 11900
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| a(n) can be represented as a figurate number using n concentric pentagons (see example). - Omar E. Pol, Aug 21 2011
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (3,-3,1).
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FORMULA
| a(n) = 5*A000326(n).
a(n) = a(n-1)+15*n-10 (with a(0)=0). - Vincenzo Librandi, Nov 26 2010
G.f.: 5*x*(1+2*x)/(1-x)^3. a(n) = 4*A000217(n)+A051865(n). - Bruno Berselli, Feb 11 2011
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EXAMPLE
| Contribution from Omar E. Pol, Aug 22 2011 (Start):
Illustration of initial terms as concentric pentagons (In a precise representation the pentagons should to be strictly concentric):
.
. o
. o o
. o o
. o o o o
. o o o o o o
. o o o o o o
. o o o o o o o o o
.o o o o o o o o o o o o
. o o o o o o o o o o o o
. o o o o o o
. o o o o o o
. o o o o o o o o o o o o
. o o
. o o
. o o o o o o o o
.
. 5 25 60
(End)
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MATHEMATICA
| s=0; lst={s}; Do[s+=n; AppendTo[lst, s], {n, 5, 7!, 15}]; lst [From Vladimir Orlovsky, Apr 03 2009]
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CROSSREFS
| Cf. A000326.
Cf. sequences of the form n*(d*n+10-d)/2 indexed in A140090.
Cf. A033581, A085250, A152751, A194275. - Omar E. Pol, Aug 21 2011
Sequence in context: A045576 A146649 A146412 * A080856 A060820 A146404
Adjacent sequences: A152731 A152732 A152733 * A152735 A152736 A152737
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KEYWORD
| easy,nonn
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AUTHOR
| Omar E. Pol (info(AT)polprimos.com), Dec 11 2008
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