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A022265 a(n) = n*(7*n + 1)/2. 14
0, 4, 15, 33, 58, 90, 129, 175, 228, 288, 355, 429, 510, 598, 693, 795, 904, 1020, 1143, 1273, 1410, 1554, 1705, 1863, 2028, 2200, 2379, 2565, 2758, 2958, 3165, 3379, 3600, 3828, 4063, 4305, 4554, 4810 (list; graph; refs; listen; history; text; internal format)
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
FORMULA
a(n) = A110449(n, 3) for n>2.
a(n) = A049453(n) - A005475(n). - Zerinvary Lajos, Jan 21 2007
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
a(n) = A000217(4*n) - A000217(3*n). - Bruno Berselli, Oct 13 2016
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
Cf. similar sequences listed in A022289.
Sequence in context: A331761 A116035 A256715 * A120389 A124150 A054556
KEYWORD
nonn,easy
AUTHOR
STATUS
approved

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Last modified June 21 05:50 EDT 2024. Contains 373540 sequences. (Running on oeis4.)