A010018 a(0) = 1, a(n) = 28*n^2 + 2 for n>0.

1, 30, 114, 254, 450, 702, 1010, 1374, 1794, 2270, 2802, 3390, 4034, 4734, 5490, 6302, 7170, 8094, 9074, 10110, 11202, 12350, 13554, 14814, 16130, 17502, 18930, 20414, 21954, 23550, 25202, 26910, 28674, 30494, 32370, 34302, 36290, 38334, 40434, 42590, 44802

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

First bisection of A005919. - Bruno Berselli, Feb 07 2012

a(n) = the second level of difference between the sum of the terms in the n+1 X n+1 matrices and those in the n X n matrices starting at n=1 for an array constructed by using the terms in A016813 as the antidiagonals; the first few antidiagonals are 1; 5,9; 13,17,21; 25,29,33,37. - J. M. Bergot, Jul 05 2013

[More formally: (sum[m(n+1),j {j=0..n+1}]+sum[m(i,n+1) {i=0..n}]) - (sum[m(n,j) {j=0...n}] + sum[m(i,n) {i=0..n-1}])=a(n)]

[The first five rows begin: 1,9,21,37,57; 5,17,33,53,77; 13,29,49,73,101;25,45,69,97,129; 41,65,93,125,161]

Links

• Bruno Berselli, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A206399.

Programs

Mathematica

Join[{1}, 28 Range[40]^2 + 2] (* Bruno Berselli, Feb 07 2012 *)
LinearRecurrence[{3, -3, 1}, {1, 30, 114, 254}, 40] (* Robert G. Wilson v, Jul 06 2013 *)

Formula

G.f.: (1+x)*(1+26*x+x^2)/(1-x)^3. - Bruno Berselli, Feb 07 2012

E.g.f.: (x*(x+1)*28+2)*e^x-1. - Gopinath A. R., Feb 14 2012

Sum_{n>=0} 1/a(n) = 3/4 + sqrt(14)/56*Pi*coth(Pi/sqrt 14) = 1.05615979263340... - R. J. Mathar, May 07 2024

a(n) = 2*A158482(n), n>0. - R. J. Mathar, May 07 2024

a(n) = A195314(n)+A195314(n+1). - R. J. Mathar, May 07 2024