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

1,1

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).

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

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 *)

Prog

(PARI) a(n)={(n^4 + 22*n^3 + 105*n^2 - 56*n - 8)/4} \\ Harry J. Smith, Jul 08 2009
(Magma) [(n^4 + 22*n^3 + 105*n^2 - 56*n - 8)/4: n in [1..40]]; // Vincenzo Librandi, Jul 03 2018

Crossrefs

Cf. A047875.

Sequence in context: A030508 A006215 A227088 * A125353 A126511 A231582

Adjacent sequences: A060630 A060631 A060632 * A060634 A060635 A060636

Keyword

easy,nonn

Author

Jason Earls, Apr 15 2001

Extensions

More terms from James A. Sellers, Apr 16 2001

Status

approved