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

Author

N. J. A. Sloane, Dec 29 2015

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A072154.

Programs

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

Mathematica

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

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

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