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

0,2

Comments

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

References

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.

Links

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).

Formula

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

Mathematica

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

Prog

(PARI) a(n)=(3+2*n+6*n^2+4*n^3)/3 \\ Charles R Greathouse IV, Oct 07 2015
(Magma) [(3+2*n+6*n^2+4*n^3)/3: n in [0..60]]; // G. C. Greubel, Jul 27 2024
(SageMath) [(3+2*n+6*n^2+4*n^3)//3 for n in range(61)] # G. C. Greubel, Jul 27 2024

Crossrefs

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

Sequence in context: A146854 A299120 A033275 * A059859 A146617 A245240

Adjacent sequences: A166461 A166462 A166463 * A166465 A166466 A166467

Keyword

nonn,easy

Author

Paul Curtz, Oct 14 2009

Extensions

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

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

Status

approved