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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The averages of four consecutive even squares are in A027575.

LINKS

Table of n, a(n) for n=1..45.

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

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.

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. - Colin Barker, Apr 15 2012

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

Adjacent sequences:  A173957 A173958 A173959 * A173961 A173962 A173963

KEYWORD

nonn,easy,changed

AUTHOR

Vladimir Joseph Stephan Orlovsky, Mar 03 2010

EXTENSIONS

Formula corrected by R. J. Mathar, Mar 31 2010

STATUS

approved

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Last modified June 27 13:28 EDT 2017. Contains 288788 sequences.