A060633 Surround numbers of an n X 1 rectangle.

16, 123, 361, 778, 1428, 2371, 3673, 5406, 7648, 10483, 14001, 18298, 23476, 29643, 36913, 45406, 55248, 66571, 79513, 94218, 110836, 129523, 150441, 173758, 199648, 228291, 259873, 294586, 332628, 374203, 419521, 468798, 522256, 580123, 642633, 710026, 782548, 860451

Offset: 1

Author

Jason Earls, Apr 15 2001

Keywords

• easy
• nonn

Links

• Harry J. Smith, Table of n, a(n) for n = 1..1000
• E. J. Friedman, Math. Magic
• Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Crossrefs

Cf. A047875.

Programs

Magma

[(n^4 + 22*n^3 + 105*n^2 - 56*n - 8)/4: n in [1..40]]; // Vincenzo Librandi, Jul 03 2018

Maple

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

Mathematica

Table[(n^4 + 22 n^3 + 105 n^2 - 56 n - 8) / 4, {n, 40}] (* Vincenzo Librandi, Jul 03 2018 *)
LinearRecurrence[{5,-10,10,-5,1},{16,123,361,778,1428},50] (* Harvey P. Dale, Dec 24 2019 *)

PARI

a(n)={(n^4 + 22*n^3 + 105*n^2 - 56*n - 8)/4} \\ Harry J. Smith, Jul 08 2009

Formula

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

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

Extensions

More terms from James Sellers, Apr 16 2001