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A059845
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n*(3*n + 11)/2.
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16
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0, 7, 17, 30, 46, 65, 87, 112, 140, 171, 205, 242, 282, 325, 371, 420, 472, 527, 585, 646, 710, 777, 847, 920, 996, 1075, 1157, 1242, 1330, 1421, 1515, 1612, 1712, 1815, 1921, 2030, 2142, 2257, 2375, 2496, 2620, 2747, 2877, 3010, 3146, 3285, 3427, 3572, 3720
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Number of Euclidean spaces for every compact Riemannian n-manifold to be realizable as a sub-manifold.
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REFERENCES
| John Nash, The Imbedding Problem For Riemannian Manifolds, Annals of Mathematics, Vol. 63, No. 1, 1956, pp. 20-63.
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LINKS
| Harry J. Smith, Table of n, a(n) for n=0,...,2000
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FORMULA
| sum (n+j-1,j=4..n). - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Sep 12 2006
a(n)=3*n+a(n-1)+4 (with a(0)=0) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Aug 07 2010]
G.f.: x*(7 - 4*x)/(1 - x)^3. [Arkadiusz Wesolowski, Dec 24 2011]
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EXAMPLE
| a(1)=3*1+0+4=7; a(2)=3*2+7+4=17; a(3)=3*3+17+4=30 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Aug 07 2010]
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MATHEMATICA
| s=0; lst={s}; Do[s+=n++ +7; AppendTo[lst, s], {n, 0, 6!, 3}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Nov 16 2008]
Table[Sum[i + n - 3, {i, 5, n}], {n, 4, 52}] [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 11 2009]
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PROG
| (PARI) { for (n=0, 2000, write("b059845.txt", n, " ", n*(3*n + 11)/2); ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jun 29 2009]
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CROSSREFS
| 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: A029532 A157417 A088566 * A006142 A196167 A001123
Adjacent sequences: A059842 A059843 A059844 * A059846 A059847 A059848
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KEYWORD
| easy,nonn
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AUTHOR
| Jason Earls (zevi_35711(AT)yahoo.com), Mar 10 2001
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