

A189890


a(n) = (n^3  2*n^2 + 3*n + 2)/2.


4



2, 4, 10, 23, 46, 82, 134, 205, 298, 416, 562, 739, 950, 1198, 1486, 1817, 2194, 2620, 3098, 3631, 4222, 4874, 5590, 6373, 7226, 8152, 9154, 10235, 11398, 12646, 13982, 15409, 16930, 18548, 20266, 22087, 24014, 26050, 28198, 30461, 32842, 35344, 37970, 40723, 43606, 46622
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

Order preserving identity difference partial one  one transformation semigroup, OIDI_n is defined if for each transformation, alpha, x<= y implies xalpha <= yalpha, for all x,y in X_n (set of natural numbers) and also the absolute value of the difference between max(Im(alpha)) and min(Im(alpha)) is less than or equal to one with nonisolation property.


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*(2+4*x6*x^2+x^3) / (x1)^4.  R. J. Mathar, Jun 20 2011
E.g.f.: 4*(2 + (2 + 2*x + x^2 + x^3)*exp(x)).  G. C. Greubel, Jan 13 2018
a(n) = 4*a(n1)6*a(n2)+4*a(n3)a(n4).  Wesley Ivan Hurt, Apr 23 2021


EXAMPLE

For n = 4, a(4) = (4^32*4^2+3*4+2)/2 = 46/2 = 23.


MATHEMATICA

Table[(n^32*n^2+3*n+2)/2, {n, 1, 50}] (* or *) LinearRecurrence[{4, 6, 4, 1}, {2, 4, 10, 23}, 50] (* G. C. Greubel, Jan 13 2018 *)


PROG

(MAGMA) [(n^32*n^2+3*n+2)/2: n in [1..50]]; // Vincenzo Librandi, May 07 2011
(PARI) a(n)=(n^32*n^2+3*n+2)/2 \\ Charles R Greathouse IV, Oct 16 2015


CROSSREFS

Cf. A188947, A188377.
Sequence in context: A337520 A173185 A294680 * A189587 A345195 A018111
Adjacent sequences: A189887 A189888 A189889 * A189891 A189892 A189893


KEYWORD

nonn,easy


AUTHOR

Adeniji, Adenike and Samuel Makanjuola(somakanjuola(AT)unilorin.edu.ng), Apr 30 2011


STATUS

approved



