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A074149 Sum of terms in each group in A074147. 6
1, 6, 15, 36, 65, 114, 175, 264, 369, 510, 671, 876, 1105, 1386, 1695, 2064, 2465, 2934, 3439, 4020, 4641, 5346, 6095, 6936, 7825, 8814, 9855, 11004, 12209, 13530, 14911, 16416, 17985, 19686, 21455, 23364, 25345, 27474, 29679, 32040, 34481, 37086 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The odd-indexed entries are the sums pertaining to the corresponding magic squares.

LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (2,1,-4,1,2,-1).

FORMULA

a(2n-1) = 4n^3 - 6n^2 + 4n - 1, a(2n) = 4n^3 + 2n. a(n) = (n^3 + n)/2 if n odd, n^3/2 + n if n even. a(n) = n^3/2 + n(3 + (-1)^n)/4. - Franklin T. Adams-Watters, Jul 17 2006

G.f.: x*(x^2+1)*(x^2+4*x+1) / ( (1+x)^2*(x-1)^4 ). - R. J. Mathar, Mar 07 2011

MATHEMATICA

LinearRecurrence[{2, 1, -4, 1, 2, -1}, {1, 6, 15, 36, 65, 114}, 50] (* Harvey P. Dale, Jun 22 2016 *)

PROG

(PARI) a(n)=n^3/2 + n*(3+(-1)^n)/4 \\ Charles R Greathouse IV, Jun 11 2015

CROSSREFS

Cf. A074147, A074148, A061925, A006003, A061804.

Sequence in context: A273861 A074132 A269543 * A273411 A273490 A324221

Adjacent sequences:  A074146 A074147 A074148 * A074150 A074151 A074152

KEYWORD

nonn,easy

AUTHOR

Amarnath Murthy, Aug 28 2002

EXTENSIONS

More terms from Franklin T. Adams-Watters, Jul 17 2006

STATUS

approved

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Last modified July 11 17:24 EDT 2020. Contains 335626 sequences. (Running on oeis4.)