A168192 a(n) = n^4*(n^2 + 1)/2.

0, 1, 40, 405, 2176, 8125, 23976, 60025, 133120, 269001, 505000, 893101, 1503360, 2427685, 3783976, 5720625, 8421376, 12110545, 17058600, 23588101, 32080000, 42980301, 56807080, 74157865, 95717376, 122265625, 154686376, 193975965

Offset

0,3

Comments

a(n) is a square for n in A002315. - Bruno Berselli, Apr 26 2012

Links

Vincenzo Librandi and Bruno Berselli, Table of n, a(n) for n = 0..1000 (First 530 terms from Vincenzo Librandi).

Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Formula

G.f.: x*(1+x)*(1+4*x+x^2)*(1+28*x+x^2)/(1-x)^7. - Bruno Berselli, Apr 26 2012

a(n) = Sum_{i=0..n^2}( A000326(i) ). - Bruno Berselli, Sep 06 2013

Mathematica

Table[(n^4 (n^2 + 1))/2, {n, 0, 27}] (* Bruno Berselli, Apr 26 2012 *)
LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {0, 1, 40, 405, 2176, 8125, 23976}, 30] (* Harvey P. Dale, Sep 22 2015 *)

Prog

(Magma) [n^4*(n^2+1)/2: n in [0..50]]; // Vincenzo Librandi, Apr 25 2011

Crossrefs

Cf. A000326, A002315.

Sequence in context: A301528 A253132 A293969 * A251129 A007772 A228122

Adjacent sequences: A168189 A168190 A168191 * A168193 A168194 A168195

Keyword

nonn,easy

Author

N. J. A. Sloane, Dec 11 2009

Status

approved