OFFSET
0,2
COMMENTS
For n >= 4, a(n) is the sum of the numbers appearing in the 4th row of an n X n square array whose elements are the numbers from 1..n^2, listed in increasing order by rows. - Wesley Ivan Hurt, May 17 2021
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..5000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
a(n) = A110449(n, 3) for n>2.
a(n) = 7*n + a(n-1) - 3 for n>0, a(0)=0. - Vincenzo Librandi, Aug 04 2010
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) with a(0)=0, a(1)=4, a(2)=15. - Philippe Deléham, Mar 26 2013
a(n) = A174738(7n+3). - Philippe Deléham, Mar 26 2013
G.f.: x*(4 + 3*x)/(1 - x)^3. - Ilya Gutkovskiy, Oct 13 2016
E.g.f.: (x/2)*(7*x + 8)*exp(x). - G. C. Greubel, Aug 23 2017
EXAMPLE
From Bruno Berselli, Oct 27 2017: (Start)
After 0:
4 = -(1) + (2 + 3).
15 = -(1 + 2) + (3 + 4 + 5 + 6).
33 = -(1 + 2 + 3) + (4 + 5 + 6 + 7 + 8 + 9).
58 = -(1 + 2 + 3 + 4) + (5 + 6 + 7 + 8 + 9 + 10 + 11 + 12). (End)
MAPLE
seq(binomial(7*n+1, 2)/7, n=0..37); # Zerinvary Lajos, Jan 21 2007
seq(binomial(6*n+1, 2)/3-binomial(5*n+1, 2)/5, n=0..42); # Zerinvary Lajos, Jan 21 2007
MATHEMATICA
Table[n (7 n + 1)/2, {n, 0, 40}] (* Bruno Berselli, Oct 13 2016 *)
LinearRecurrence[{3, -3, 1}, {0, 4, 15}, 40] (* Harvey P. Dale, Oct 09 2018 *)
PROG
(PARI) a(n)=n*(7*n+1)/2 \\ Charles R Greathouse IV, Oct 07 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved