A175828 a(n) = (n*(6*n+1)+(n+2)*(-1)^n)/2.

1, 2, 15, 26, 53, 74, 115, 146, 201, 242, 311, 362, 445, 506, 603, 674, 785, 866, 991, 1082, 1221, 1322, 1475, 1586, 1753, 1874, 2055, 2186, 2381, 2522, 2731, 2882, 3105, 3266, 3503, 3674, 3925, 4106, 4371, 4562, 4841, 5042, 5335, 5546, 5853, 6074

Offset: 0

Author

Bruno Berselli, Sep 21 2010 - Sep 25 2010

Keywords

• nonn
• easy

Comments

a(n) == A068073(n) (mod 4).

a(h) == 0 (mod 11) for h = 11*(k-floor((k-1)/3))-2*(-1)^(k+floor(k/3)) (cf. A175833).

Links

• Bruno Berselli, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (1,2,-2,-1,1).

Crossrefs

Cf. A068073, A010718, A142241, A175833.

Programs

Magma

[(n*(6*n+1)+(n+2)*(-1)^n)/2: n in [0..50]];

Magma

I:=[1,2,15,26,53]; [n le 5 select I[n] else Self(n-1)+2*Self(n-2)-2*Self(n-3)-Self(n-4)+Self(n-5): n in [1..50]]; // Vincenzo Librandi, Aug 19 2013

Mathematica

Table[(n (6 n + 1) + (n + 2) (-1)^n)/2, {n, 0, 50}]
CoefficientList[Series[(1 + x + 11 x^2 + 9 x^3 + 2 x^4) / ((1 + x)^2 (1 - x)^3), {x, 0, 50}], x] (* Vincenzo Librandi, Aug 19 2013 *)
LinearRecurrence[{1,2,-2,-1,1},{1,2,15,26,53},70] (* Harvey P. Dale, Jul 03 2019 *)

Formula

G.f.: (1+x+11*x^2+9*x^3+2*x^4)/((1+x)^2*(1-x)^3).

a(n)-a(n-1)-2*a(n-2)+2*a(n-3)+a(n-4)-a(n-5) = 0 for n>4.

a(n)-a(n-2)-(a(n-1)-a(n-3)) = 2*A010718(n-1) for n>2.

a(n)-a(n-2)+(a(n-1)-a(n-3)) = A142241(n-2) for n>2.