A018227 -id:A018227 - cp's OEIS frontend

A166464 a(n) = (3 + 2n + 6n^2 + 4*n^3)/3.

1, 5, 21, 57, 121, 221, 365, 561, 817, 1141, 1541, 2025, 2601, 3277, 4061, 4961, 5985, 7141, 8437, 9881, 11481, 13245, 15181, 17297, 19601, 22101, 24805, 27721, 30857, 34221, 37821, 41665, 45761, 50117, 54741, 59641, 64825, 70301, 76077, 82161, 88561, 95285, 102341, 109737, 117481, 125581

Offset: 0

Paul Curtz, Oct 14 2009

Atomic number of first transition metal of period 2n (n>3) or of the element after n-th alkaline earth metal. This can be calculated by finding the sum of the first n even squares plus 1. - Natan Arie Consigli, Jul 03 2016

JANET,Charles, La structure du Noyau de l'atome,consideree dans la Classification periodique,des elements chimiques,1927 (Novembre),N. 2,BEAUVAIS,67 pages,3 leaflets.

G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Cf. A002492, A010731, A016742, A017113, A018227.

[(3+2*n+6*n^2+4*n^3)/3: n in [0..60]]; // G. C. Greubel, Jul 27 2024

Table[(3+2*n+6*n^2+4*n^3)/3, {n,0,60}] (* G. C. Greubel, May 15 2016 *)

a(n)=(3+2*n+6*n^2+4*n^3)/3 \\ Charles R Greathouse IV, Oct 07 2015

[(3+2*n+6*n^2+4*n^3)//3 for n in range(61)] # G. C. Greubel, Jul 27 2024

a(n) - a(n-1) = 4*(n+1)^2 = A016742(n+1).
a(n) - 2*a(n-1) + a(n-2) = -4 + 8*n = A017113(n+1).
a(n) - 3*a(n-1) + 3*a(n-2) - a(n-3) = 8 = A010731(n).
a(n) - 4*a(n-1) + 6*a(n-2) - 4*a(n-3) + a(n-4) = 0.
Binomial transform of quasi-finite sequence 1,4,12,8,0,(0 continued).
G.f.: (1+x+7*x^2-x^3)/(1-x)^4. - R. J. Mathar, Feb 15 2010
From Natan Arie Consigli, Jul 03 2016: (Start)
a(n) = A018227(2*n) + 3.
a(n) = A002492(n) + 1. (End)
E.g.f.: (1/3)*(3 + 12*x + 18*x^2 + 4*x^3)*exp(x). - G. C. Greubel, Jul 27 2024

Edited by N. J. A. Sloane, Oct 17 2009

More terms a(11)-a(35) from Vincenzo Librandi, Oct 17 2009

A099956 Atomic numbers of the alkaline earth metals.

Original entry on oeis.org

4, 12, 20, 38, 56, 88

Offset: 1

Parthasarathy Nambi, Nov 12 2004

			12 is the atomic number of magnesium.

Cf. A099955, alkali metals; A101648, metalloids; A101647, nonmetals (except halogens and noble gases); A097478, halogens; A018227, noble gases; A101649, poor metals.

A101649 Atomic numbers of the poor metals on the periodic table.

Original entry on oeis.org

13, 31, 49, 50, 81, 82, 83

Offset: 1

Robert Happelberg (roberthappelberg(AT)yahoo.com), Dec 10 2004

Elements 113, 114 and 115 are believed to be poor metals too. Element 116 could be either a poor metal or a metalloid. So I'm not putting the keyword full at this time. The poor metals are between the metalloids and the transition metals on the periodic table.

			The atomic number of aluminium is 13.

The New Encyclopaedia Britannica, 15th Edition, 1991, Volume 15 (Macropedia), Chemical Elements.

International Union of Pure and Applied Chemistry, Periodic Table of Elements
Wikipedia, Periodic table.
Wikipedia, Poor metals.

Cf. A099955, alkali metals; A099956, alkaline earth metals; A101648, metalloids; A101647, nonmetals (except halogens and noble gases); A097478, halogens; A018227, noble gases; A101649, poor metals.

A097478 Atomic numbers of halogens in the periodic table.

Original entry on oeis.org

9, 17, 35, 53, 85, 117

Offset: 1

Parthasarathy Nambi, Sep 19 2004

nonn

The halogens are all on the second rightmost column of the periodic table. (The rightmost column belongs to the noble gases.) - Alonso del Arte, Apr 26 2011

Halogens: 9, fluorine (F); 17;,chlorine (Cl); 35, bromine (Br); 53, iodine (I); 85, astatine (At); and 117, tennessine (Ts). - Daniel Forgues, Jul 13 2015, Luca Khan, Sep 09 2024

Monica Halka and Brian Nordstrom, Halogens and Noble Gases, Facts On File (2010), Part 1: The Halogens.

Bodner Research Web, The Chemistry of the Halogens
Royal Society of Chemistry, Periodic Table, 2015.
Wikipedia, Halogen

Cf. A099955, alkali metals; A099956, alkaline earth metals; A101648, metalloids; A101647, nonmetals (except halogens and noble gases); A018227, noble gases; A101649, poor metals.

a(1) = 9; a(n) = a(n-1) + 2 * (ceiling(n/2) + 1)^2, 2 <= n <= 6.

A101647 Atomic numbers of elements excluding metals, halogens, and noble gases in the periodic table.

Original entry on oeis.org

1, 6, 7, 8, 15, 16, 34

Offset: 1

Robert Happelberg (roberthappelberg(AT)yahoo.com), Dec 10 2004

"Nonmetals" as normally understood in elementary chemistry.
All nonmetals are sandwiched between the halogens and metalloids on the periodic table, with the exception of hydrogen, which is on the same group as the alkali metals. - Happelberg
There may appear to be some disagreement in regards to the definition of nonmetals. This sequence appears on the cover of the Halka and Nordstrom book on nonmetals, and that book has eight chapters, the first seven of which are each devoted to an element identified by this sequence.
The Baldwin book, on the other hand, flatly declares "All elements to the right of the stepped line [on the periodic table shown in that book] are nonmetals," meaning that the author also considers halogens and noble gases to be nonmetals.
But then there is the Halka and Nordstrom book on halogens and noble gases, which says "The halogens ... are nonmetals, but have such special properties that they are given their own classification. The same is true for the noble gases." - Alonso del Arte, Apr 26 2011

			Carbon is a nonmetal, and its atomic number is 6.

Carol Baldwin, Nonmetals. Raintree (2006) p. 13
Monica Halka and Brian Nordstrom, Halogens and Noble Gases, Facts On File (2010), p. xiii
Monica Halka and Brian Nordstrom, Nonmetals, Facts On File (2010)
The New Encyclopaedia Britannica, 15th Edition, 1991, Volume 15 (Macropedia), Chemical Elements.

Yinon Benton, Periodic Table: Non-Metals, from ChemicalElements.com.
Bodner Research Web, The Chemistry Of Nonmetals, from the Purdue University College of Science.
Wikipedia, Nonmetals.

Cf. A099955 (alkali metals), A099956 (alkaline earth metals), A101648 (metalloids), A097478 (halogens), A018227 (noble gases), A101649 (poor metals).

A101648 Atomic numbers of the metalloids or semimetals on the periodic table.

Original entry on oeis.org

5, 14, 32, 33, 51, 52, 84

Offset: 1

Robert Happelberg (roberthappelberg(AT)yahoo.com), Dec 10 2004

If ununhexium and ununseptium turn out to be metalloids, 116 and 117 should be added to this sequence, so I'm not putting the keyword full at this time. The metalloids are sandwiched between the nonmetals and the poor metals on the periodic table.

			The atomic number of boron is 5.

The New Encyclopaedia Britannica, 15th Edition, 1991, Volume 15 (Macropedia), Chemical Elements.

Wikipedia, Periodic table.
Wikipedia, Metalloids.

Cf. A099955, alkali metals; A099956, alkaline earth metals; A101647, nonmetals (except halogens and noble gases); A097478, halogens; A018227, noble gases; A101649, poor metals.

A137904 Rows 1, 3, 5, 7 of Mendeleyev-Seaborg (extended to 32 columns) periodic table elements.

Original entry on oeis.org

1, 2, 11, 12, 13, 14, 15, 16, 17, 18, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118

Offset: 0

Paul Curtz, Apr 30 2008

60 terms. See A137575 (58 terms for rows 2, 4, 6). Differences 9, 19, 33 leads to difference 3 before a(1)=1. Hence -2, antihelium. Like A137583, 2, 2, 8 for A018227, 2, 10, 18, "magic numbers".

R. Arsenescu, Antihelium-3 production in lead-lead collisions at 158 A GeV/c. New Journal of Physics 5:1,2003. doi:10.1088/1367-2630/5/1/301.

Cf. A134984, A137913.

A058318 Number of energy levels in atoms of the n-th element of the periodic table.

Original entry on oeis.org

1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7

Offset: 1

Labos Elemer, Dec 12 2000

Run lengths, i.e., how many elements have 1,2,3,4,5,6,7 energy levels, are 2,8,8,18,18,32,26 (see A137583).

			For n=79, element 79 (Gold) has a(79)=6 energy levels (which may have 2,8,18,32,18,1 electrons).

Y. Bentor, Chemical Elements.Com
M. Winter, WebElements Periodic Table.

Cf. A007656, A018227, A058317, A137583, A173592.

seq(i$[2, 8, 8, 18, 18, 32, 32][i], i=1..7); # Michel Lagneau, Apr 03 2024

a(n) = m for s(m-1) < n <= s(m) for m=1..7, where s(m) = A173592(m) and s(0) = 0. - Michel Lagneau, Apr 03 2024

a(106)-a(118) from Michel Lagneau, Apr 03 2024

A277131 Magic numbers of anti-Mackay icosahedra.

Original entry on oeis.org

45, 127, 279, 521, 873, 1355, 1987, 2789, 3781, 4983, 6415, 8097, 10049, 12291, 14843, 17725, 20957, 24559, 28551, 32953, 37785, 43067, 48819, 55061, 61813, 69095, 76927, 85329, 94321, 103923, 114155, 125037, 136589, 148831, 161783, 175465, 189897, 205099

Offset: 2

Felix Fröhlich, Oct 01 2016

Colin Barker, Table of n, a(n) for n = 2..1000
D. Bochicchio and R. Ferrando, Size-Dependent Transition to High-Symmetry Chiral Structures in AgCu, AgCo, AgNi, and AuNi Nanoalloys, Nano Letters, Vol. 10, No. 10 (2010), 4211-4216.
Index entries for sequences related to magic numbers
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Cf. A005902, A008592, A018226, A018227.

A277131:=n->11-(19*n)/3+5*n^2+(10*n^3)/3: seq(A277131(n), n=2..50); # Wesley Ivan Hurt, Oct 07 2016

DeleteCases[CoefficientList[Series[x^2*(45 - 53 x + 41 x^2 - 13 x^3)/(1 - x)^4, {x, 0, 39}], x], 0] (* Michael De Vlieger, Oct 02 2016 *)

a(n) = (2*n+1) * (5*n^2+5*n+3) / 3 - 10*(n-1)

Vec(x^2*(45-53*x+41*x^2-13*x^3)/(1-x)^4 + O(x^50)) \\ Colin Barker, Oct 01 2016

a(n) = A005902(n) - A008592(n-1).
a(n) = 10/3*n^3 + 25*n^2 + 161/3*n + 45 with offset 0.
From Colin Barker, Oct 01 2016: (Start)
a(n) = 4*a(n-1)-6*a(n-2)+4*a(n-3)-a(n-4) for n>5.
a(n) = 11-(19*n)/3+5*n^2+(10*n^3)/3.
G.f.: x^2*(45-53*x+41*x^2-13*x^3) / (1-x)^4.
(End)

A230434 Magic numbers of nucleons. Another version of A018226, with 34 inserted.

Original entry on oeis.org

2, 8, 20, 28, 34, 50, 82, 126

Offset: 1

Omar E. Pol, Oct 22 2013

Union of 34 and A018226.

D. Steppenbeck et al., Evidence for a new nuclear 'magic number' from the level structure of 54Ca, Nature, 502 (2013), 207-210, DOI: 10.1038/nature12522.

Cf. A018226, A018227, A033547, A046939, A046940, A110856, A117612.

cp's OEIS Frontend

A166464 a(n) = (3 + 2*n + 6*n^2 + 4*n^3)/3.

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A099956 Atomic numbers of the alkaline earth metals.

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A101649 Atomic numbers of the poor metals on the periodic table.

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A097478 Atomic numbers of halogens in the periodic table.

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A101647 Atomic numbers of elements excluding metals, halogens, and noble gases in the periodic table.

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A101648 Atomic numbers of the metalloids or semimetals on the periodic table.

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A137904 Rows 1, 3, 5, 7 of Mendeleyev-Seaborg (extended to 32 columns) periodic table elements.

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A058318 Number of energy levels in atoms of the n-th element of the periodic table.

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A277131 Magic numbers of anti-Mackay icosahedra.

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A166464 a(n) = (3 + 2n + 6n^2 + 4*n^3)/3.