A219527 a(n) = (6*n^2 + 7*n - 9 + 2*n^3)/12 - (-1)^n*(n+1)/4.

1, 3, 11, 19, 37, 55, 87, 119, 169, 219, 291, 363, 461, 559, 687, 815, 977, 1139, 1339, 1539, 1781, 2023, 2311, 2599, 2937, 3275, 3667, 4059, 4509, 4959, 5471, 5983, 6561, 7139, 7787, 8435, 9157, 9879, 10679, 11479, 12361, 13243

Offset: 1

Author

Paul Curtz, Nov 21 2012

Keywords

• nonn
• easy

Comments

First column of the Mendeleyev-Moseley-Seaborg table (with alkali metals) or 31st column of the Janet table. See A138726.

(a(n+10) - a(n))/10 = 29, 36, 45, 54, ... = A061925(n+7) + 3.

b(n) = a(n+1) - 2*a(n) = 1, 5, -3, -1, -19, -23, -55, -69, -119, -147, -219, -265, -363, -431, ... contains -a(2*n).

b(2*n-1) - b(2*n-2) = 4, 2, -4, -14, -28, -46, -68, ... = A147973(n+3).

Links

• Index entries for linear recurrences with constant coefficients, signature (2,1,-4,1,2,-1).

Crossrefs

Cf. A147973.

Programs

Mathematica

a[n_] := (6*n^2 + 7*n - 9 + 2*n^3)/12 - (-1)^n*(n + 1)/4; Table[ a[n], {n, 1, 42}] (* Jean-François Alcover, Apr 05 2013 *)
LinearRecurrence[{2,1,-4,1,2,-1},{1,3,11,19,37,55},50] (* Harvey P. Dale, Apr 01 2018 *)

Formula

a(n) = A168380(n+1) - 1.

a(n+2) - a(n+1) = A093907(n) = A137583(n+1).

a(n+3) - a(n+1) = 10,16,26,36,... = A137928(n+3).

G.f. x*(1 + x + 4*x^2 - 2*x^3 + x^5 - x^4) / ( (1+x)^2*(x-1)^4 ). - R. J. Mathar, Mar 27 2013