OFFSET
0,2
COMMENTS
A142241 gives the first differences.
Inverse binomial transform of this sequence: 1, 14, 24, 0, 0 (0 continued).
a(n)*a(n-1)-11 is a square, precisely 4*A051866(n)^2.
Sequence found by reading the line from 1, in the direction 1, 15, ..., in the square spiral whose vertices are the generalized octagonal numbers A001082. - Omar E. Pol, Jul 18 2012
LINKS
Bruno Berselli, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
G.f.: (1+x)*(1+11*x)/(1-x)^3.
a(n) = A154106(-n-1).
a(n) = 2*A049453(n) + 1.
E.g.f.: exp(x)*(1 + 14*x + 12*x^2). - Stefano Spezia, Nov 15 2019
EXAMPLE
Using these numbers we can write:
1, 15, 53, 115, 201, 311, 445, 603, 785, 991, 1221, ...
0, 0, 1, 15, 53, 115, 201, 311, 445, 603, 785, ...
0, 0, 0, 0, 1, 15, 53, 115, 201, 311, 445, ...
0, 0, 0, 0, 0, 0, 1, 15, 53, 115, 201, ...
0, 0, 0, 0, 0, 0, 0, 0, 1, 15, 53, ...
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, ...
======================================================
The sums of the columns give the sequence A172073 (after 0):
1, 15, 54, 130, 255, 441, 700, 1044, 1485, 2035, 2706, ...
MATHEMATICA
Table[12 n^2 + 2 n + 1, {n, 0, 50}] (* Vincenzo Librandi, Mar 26 2013 *)
PROG
(Magma) [12*n^2+2*n+1: n in [0..40]];
(PARI) for(n=0, 40, print1(12*n^2+2*n+1", "));
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Bruno Berselli, Aug 24 2011
STATUS
approved