

A003777


a(n) = n^3 + n^2  1.


5



1, 11, 35, 79, 149, 251, 391, 575, 809, 1099, 1451, 1871, 2365, 2939, 3599, 4351, 5201, 6155, 7219, 8399, 9701, 11131, 12695, 14399, 16249, 18251, 20411, 22735, 25229, 27899, 30751, 33791, 37025, 40459, 44099, 47951, 52021, 56315, 60839, 65599, 70601, 75851
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OFFSET

1,2


COMMENTS

This sequence in related to A095794 by a(n) = n*A095794(n)  Sum_{i=1..n1} A095794(i), for n > 1.  Bruno Berselli, Dec 28 2010
a(n) is the area of a triangle with vertices at points (n1,(n1)^2), (n,n^2), and ((n+1)^2,n+1).  J. M. Bergot, Jun 03 2014
Old name was: "Number of stacks of n pikelets, distance 3 flips from a wellordered stack".


LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (4,6,4,1).


FORMULA

G.f.: x*(1+7*x3*x^2+x^3)/(1x)^4. Also, a(n) = 2*A002411(n)  1 = A000578(n1) + A001107(n).  Bruno Berselli, Dec 28 2010
a(n) = 4*a(n1)  6*a(n2) + 4*a(n3)  a(n4) for n > 4.  Wesley Ivan Hurt, Oct 08 2017


MAPLE

A003777:=n>n^3+n^21; seq(A003777(n), n=1..50); # Wesley Ivan Hurt, Jun 04 2014


MATHEMATICA

Table[n^3+n^21, {n, 100}] (* Vladimir Joseph Stephan Orlovsky, Mar 09 2011 *)
CoefficientList[Series[(1 + 7 x  3 x^2 + x^3) / (1  x)^4, {x, 0, 50}], x] (* Vincenzo Librandi, Jun 20 2013 *)


PROG

(MAGMA) [(n^3+n^21): n in [1..50]]; // Vincenzo Librandi, Apr 06 2011
(PARI) a(n)=n^3+n^21 \\ Charles R Greathouse IV, Oct 07 2015


CROSSREFS

Cf. A000578, A001107, A002411, A095794.
Sequence in context: A233546 A092069 A103115 * A222512 A297539 A323691
Adjacent sequences: A003774 A003775 A003776 * A003778 A003779 A003780


KEYWORD

nonn,easy


AUTHOR

N. J. A. Sloane, Jun 14 1998


EXTENSIONS

More terms from Wesley Ivan Hurt, Jun 04 2014
Entry revised by N. J. A. Sloane, Jun 15 2014


STATUS

approved



