OFFSET
0,2
COMMENTS
This sequence is related to A050441 by n*a(n) - Sum_{i=0..n-1} a(i) = 2*A050441(n). - Bruno Berselli, Aug 19 2010
Sum of n-th heptagonal number (A000566) and n-th octagonal number (A000567). - Bruno Berselli, Jun 11 2013
Create a triangle with T(r,1) = r^2 and T(r,c) = r^2 + r*c + c^2. The difference of the sum of the terms in row n and those in row n-1 is a(n). - J. M. Bergot, Jun 17 2013
LINKS
B. Berselli, Table of n, a(n) for n = 0..10000.
B. Berselli, A description of the recursive method in Comments lines: website Matem@ticamente (in Italian).
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
G.f.: x*(2+9*x)/(1-x)^3. - Bruno Berselli, Aug 19 2010 - corrected in Apr 18 2011
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) with n>2. - Bruno Berselli, Aug 19 2010
a(n) = n + A226492(n). - Bruno Berselli, Jun 11 2013
E.g.f.: x*(4 + 11*x)*exp(x)/2. - G. C. Greubel, Aug 24 2015
MAPLE
MATHEMATICA
Table[(11*n^2 - 7*n)/2, {n, 0, 30}] (* Wesley Ivan Hurt, Feb 25 2014 *)
LinearRecurrence[{3, -3, 1}, {0, 2, 15}, 50] (* Harvey P. Dale, Oct 10 2020 *)
PROG
(PARI) a(n)=1/2*(11*n^2 - 7*n);
(Magma) [(11*n^2 - 7*n)/2: n in [0..30]]; // Vincenzo Librandi, Apr 18 2011
(Sage) [n*(11*n-7)/2 for n in (0..30)] # G. C. Greubel, Sep 18 2019
(GAP) List([0..30], n-> n*(11*n-7)/2); # G. C. Greubel, Sep 18 2019
CROSSREFS
Cf. numbers of the form n*(n*k-k+4)/2 listed in A226488 (this sequence is the case k=11). - Bruno Berselli, Jun 10 2013
KEYWORD
nonn,easy
AUTHOR
Graziano Aglietti (mg5055(AT)mclink.it), Aug 16 2010
STATUS
approved