A265078 Partial sums of A072154.

1, 4, 9, 16, 25, 37, 52, 69, 88, 109, 133, 160, 189, 220, 253, 289, 328, 369, 412, 457, 505, 556, 609, 664, 721, 781, 844, 909, 976, 1045, 1117, 1192, 1269, 1348, 1429, 1513, 1600, 1689, 1780, 1873, 1969, 2068, 2169, 2272, 2377, 2485, 2596, 2709, 2824, 2941, 3061, 3184, 3309, 3436, 3565, 3697

Offset

0,2

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (2,-1,0,0,1,-2,1).

Formula

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

a(n) = 2*a(n-1) - a(n-2) + a(n-5) - 2*a(n-6) + a(n-7). - Vincenzo Librandi, Jan 01 2016

Mathematica

LinearRecurrence[{2, -1, 0, 0, 1, -2, 1}, {1, 4, 9, 16, 25, 37, 52}, 60] (* Vincenzo Librandi, Jan 01 2016 *)

Prog

(PARI) Vec((1+x)^2*(1-x+x^2)*(1+x+x^2)/((1-x)^3*(1+x+x^2+x^3+x^4)) + O(x^70)) \\ Colin Barker, Jan 01 2016
(Magma) I:=[1, 4, 9, 16, 25, 37, 52]; [n le 7 select I[n] else 2*Self(n-1)-Self(n-2)+Self(n-5)-2*Self(n-6)+Self(n-7): n in [1..60]]; // Vincenzo Librandi, Jan 01 2016

Crossrefs

Cf. A072154.

Sequence in context: A254073 A075056 A022779 * A266782 A008105 A008089

Adjacent sequences: A265075 A265076 A265077 * A265079 A265080 A265081

Keyword

nonn,easy

Author

N. J. A. Sloane, Dec 29 2015

Status

approved