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A173960
Averages of four consecutive odd squares.
5
21, 41, 69, 105, 149, 201, 261, 329, 405, 489, 581, 681, 789, 905, 1029, 1161, 1301, 1449, 1605, 1769, 1941, 2121, 2309, 2505, 2709, 2921, 3141, 3369, 3605, 3849, 4101, 4361, 4629, 4905, 5189, 5481, 5781, 6089, 6405, 6729, 7061, 7401, 7749, 8105, 8469
OFFSET
1,1
COMMENTS
The averages of four consecutive even squares are in A027575.
FORMULA
a(n) = ((2*n-1)^2 + (2*n+1)^2 + (2*n+3)^2 + (2*n+5)^2)/4 = 4*n^2 + 8*n + 9.
From Colin Barker, Apr 15 2012: (Start)
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
G.f.: x*(21-22*x+9*x^2)/(1-x)^3. (End)
E.g.f.: exp(x)*(4*x^2 + 12*x + 9) - 9. - Elmo R. Oliveira, Nov 01 2024
EXAMPLE
(1^2 + 3^2 + 5^2 + 7^2)/4 = 21.
MAPLE
A173960 := proc(n) 4*n^2+8*n+9 ; end proc: seq(A173960(n), n=1..100) ; # R. J. Mathar, Mar 31 2010
MATHEMATICA
f[n_]:=(n^2+(n+2)^2+(n+4)^2+(n+6)^2)/4; Table[f[n], {n, 1, 6!, 2}]
PROG
(PARI) a(n)=4*n^2+8*n+9 \\ Charles R Greathouse IV, Jun 17 2017
CROSSREFS
Cf. A027575.
Sequence in context: A261522 A215145 A154576 * A147273 A195034 A067344
KEYWORD
nonn,easy,changed
AUTHOR
EXTENSIONS
Formula corrected by R. J. Mathar, Mar 31 2010
STATUS
approved