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A166464
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a(n) = (3+2n+6n^2+4n^3)/3.
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10
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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
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OFFSET
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0,2
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COMMENTS
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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
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REFERENCES
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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.
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LINKS
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FORMULA
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a(n) = a(n-1)+4+8n+4n^2 or a(n)-a(n-1)=4*(n+1)^2 = A016742(n+1).
a(n) = 2a(n-1)-a(n-2)-4+8n or a(n)-2a(n-1)+a(n-2)=-4+8n = A017113(n+1).
a(n) = 3a(n-1)-3a(n-2)+a(n-3)+8 or a(n)-3a(n-1)+3a(n-2)-a(n-3)=8 =A010731.
a(n) = 4a(n-1)-6a(n-2)+4a(n-3)-a(n-4) or a(n)-4a(n-1)+6a(n-2)-4a(n-3)+a(n-4)=0 = A000004(n).
Binomial transform of quasi-finite sequence 1,4,12,8,0,(0 continued).
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MATHEMATICA
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Table[(3 + 2*n + 6*n^2 + 4*n^3)/3, {n, 0, 100}](* G. C. Greubel, May 15 2016 *)
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PROG
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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