A060633 - OEIS

%I #31 Sep 08 2022 08:45:03

%S 16,123,361,778,1428,2371,3673,5406,7648,10483,14001,18298,23476,

%T 29643,36913,45406,55248,66571,79513,94218,110836,129523,150441,

%U 173758,199648,228291,259873,294586,332628,374203,419521,468798,522256,580123,642633,710026,782548,860451

%N Surround numbers of an n X 1 rectangle.

%H Harry J. Smith, <a href="/A060633/b060633.txt">Table of n, a(n) for n = 1..1000</a>

%H E. J. Friedman, <a href="https://erich-friedman.github.io/mathmagic/0599.html">Math. Magic</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).

%F a(n) = (n^4 + 22*n^3 + 105*n^2 - 56*n - 8)/4.

%F G.f.: x*(-16 - 43*x + 94*x^2 - 43*x^3 + 2*x^4) / (x-1)^5. - _R. J. Mathar_, Jan 30 2011

%p for n from 1 to 50 do printf(`%d,`,(n^4+22*n^3+105*n^2-56*n-8)/4) od:

%t Table[(n^4 + 22 n^3 + 105 n^2 - 56 n - 8) / 4, {n, 40}] (* _Vincenzo Librandi_, Jul 03 2018 *)

%t LinearRecurrence[{5,-10,10,-5,1},{16,123,361,778,1428},50] (* _Harvey P. Dale_, Dec 24 2019 *)

%o (PARI) a(n)={(n^4 + 22*n^3 + 105*n^2 - 56*n - 8)/4} \\ _Harry J. Smith_, Jul 08 2009

%o (Magma) [(n^4 + 22*n^3 + 105*n^2 - 56*n - 8)/4: n in [1..40]]; // _Vincenzo Librandi_, Jul 03 2018

%Y Cf. A047875.

%K easy,nonn

%O 1,1

%A _Jason Earls_, Apr 15 2001

%E More terms from _James A. Sellers_, Apr 16 2001