

A154105


a(n) = 12*n^2 + 18*n + 7.


4



7, 37, 91, 169, 271, 397, 547, 721, 919, 1141, 1387, 1657, 1951, 2269, 2611, 2977, 3367, 3781, 4219, 4681, 5167, 5677, 6211, 6769, 7351, 7957, 8587, 9241, 9919, 10621, 11347, 12097, 12871, 13669, 14491, 15337, 16207, 17101, 18019, 18961, 19927, 20917, 21931
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,1


COMMENTS

a(n) is the number of partitions with three integral dissimilar components of the number 12(n+1), e.g for n=0, 12 may be partitioned in the 7 ways (1,2,9), (1,3,8), (1,4,7), (1,5,6), (2,3,7), (2,4,6) and (3,4,5).  Ian Duff, Jan 31 2010
Sequence found by reading the line from 7, in the direction 7, 37, ..., in the square spiral whose vertices are the generalized octagonal numbers A001082.  Omar E. Pol, May 08 2018


LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..3000
Index entries for linear recurrences with constant coefficients, signature (3,3,1).


FORMULA

G.f.: (7 + 16*x + x^2)/(1x)^3.
a(n) = 6*A014106(n) + 7.
a(0) = 7; for n > 0, a(n) = a(n1) + 24*n + 6.
a(n1) = 2*A085473(n)  1.  Bruno Berselli, Sep 05 2011
E.g.f.: (7 + 30*x + 12*x^2)*exp(x).  G. C. Greubel, Sep 02 2016
a(n) = 1 + A152746(n+1).  Omar E. Pol, May 08 2018


EXAMPLE

a(2) = 12*2^2 + 18*2 + 7 = 91 = 6*14 + 7 = 6*A014106(2) + 7.
a(3) = a(2) + 24*3 + 6 = 91 + 72 + 6 = 169.
a(4) = 12*4^2  18*4 + 7 = 127 = 2*64  1 = 2*A085473(3)  1.


MATHEMATICA

Table[12*n^2 + 18*n + 7, {n, 0, 42}] (* Vladimir Joseph Stephan Orlovsky, Feb 20 2012 *)
LinearRecurrence[{3, 3, 1}, {7, 37, 91}, 25] (* G. C. Greubel, Sep 02 2016 *)


PROG

(MAGMA) [ 12*n^2+18*n+7: n in [0..40] ];
(PARI) a(n)=12*n^2+18*n+7 \\ Charles R Greathouse IV, Sep 02 2016


CROSSREFS

Cf. A001082, A014106, A152746, A153286, A085473.
Sequence in context: A031395 A138906 A107938 * A159491 A106064 A282001
Adjacent sequences: A154102 A154103 A154104 * A154106 A154107 A154108


KEYWORD

nonn,easy


AUTHOR

Klaus Brockhaus, Jan 04 2009


STATUS

approved



