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A051673
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Cubic star numbers: a(n)=n^3+4*sum(i^2,i=0..n-1).
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5
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0, 1, 12, 47, 120, 245, 436, 707, 1072, 1545, 2140, 2871, 3752, 4797, 6020, 7435, 9056, 10897, 12972, 15295, 17880, 20741, 23892, 27347, 31120, 35225, 39676, 44487, 49672, 55245, 61220, 67611, 74432, 81697, 89420, 97615, 106296, 115477, 125172
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Also as a(n)=(1/6)*(14*n^3-12*n^2+4*n), n>0: structured cubeoctahedral numbers (vertex structure 7); and structured pentagonal anti-diamond numbers (vertex structure 7) (Cf. A004466 = alternate vertex) (Cf. A100188 = structured anti-diamonds). Cf. A100145 for more on structured polyhedral numbers. - James A. Record (james.record(AT)gmail.com), Nov 7, 2004.
Starting with offset 1 = binomial transform of [1, 11, 24, 14, 0, 0, 0,...]. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Aug 05 2009
This is prime for a(3) = 47. The subsequence of semiprimes begins: 707, 7435, 10897, 20741, 115477, 341797, 825091, 897097, no more through a(100). - Jonathan Vos Post (jvospost3(AT)gmail.com), May 27 2010
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REFERENCES
| T. A. Gulliver, Sequences from Arrays of Integers, Int. Math. Journal, Vol. 1, No. 4, pp. 323-332, 2002.
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index to sequences with linear recurrences with constant coefficients, signature (4,-6,4,-1).
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FORMULA
| a(n)=n*(n*(7*n-6)+2)/3.
G.f.: x*(1+8*x+5*x^2)/(1-x)^4 - Bruno Berselli, May 12 2011
a(0)=0, a(1)=1, a(2)=12, a(3)=47, a(n)=4*a(n-1)-6*a(n-2)+ 4*a(n-3)- a(n-4) [From Harvey P. Dale, Jul 22 2011]
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EXAMPLE
| a(51) = 51*(51*(7*51-6)+2)/3 = 304351 = 17 * 17903 is semiprime. [From Jonathan Vos Post (jvospost3(AT)gmail.com), May 27 2010]
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MATHEMATICA
| Table[n^3+4Sum[i^2, {i, 0, n-1}], {n, 0, 40}] (* or *) LinearRecurrence[ {4, -6, 4, -1}, {0, 1, 12, 47}, 40] (* From Harvey P. Dale, Jul 22 2011 *)
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PROG
| (MAGMA) [n*(n*(7*n-6)+2)/3: n in [0..50]]; // Vincenzo Librandi, May 12 2011
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CROSSREFS
| A051662, A005915.
Sequence in context: A159013 A022281 A024183 * A030623 A030624 A002612
Adjacent sequences: A051670 A051671 A051672 * A051674 A051675 A051676
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KEYWORD
| easy,nice,nonn
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AUTHOR
| Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de)
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EXTENSIONS
| Corrected by T. D. Noe (noe(AT)sspectra.com), Nov 01 2006, Nov 08 2006
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