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A074149
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Sum of terms in each group in A074147.
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6
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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
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OFFSET
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1,2
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COMMENTS
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The odd-indexed entries are the sums pertaining to the corresponding magic squares.
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LINKS
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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).
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FORMULA
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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
E.g.f.: x*((2 + 3*x + x^2)*cosh(x) + (3 + 3*x + x^2)*sinh(x))/2. - Stefano Spezia, May 07 2021
a(n) = n*(n^2-A000035(n))/2 + n. - Chai Wah Wu, Aug 30 2022
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MATHEMATICA
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LinearRecurrence[{2, 1, -4, 1, 2, -1}, {1, 6, 15, 36, 65, 114}, 50] (* Harvey P. Dale, Jun 22 2016 *)
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PROG
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(PARI) a(n)=n^3/2 + n*(3+(-1)^n)/4 \\ Charles R Greathouse IV, Jun 11 2015
(Python)
def A074149(n): return (n*(n**2-(n&1))>>1)+n # Chai Wah Wu, Aug 30 2022
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CROSSREFS
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Cf. A000035, A074147, A074148, A061925, A006003, A061804.
Sequence in context: A273861 A074132 A269543 * A273411 A273490 A324221
Adjacent sequences: A074146 A074147 A074148 * A074150 A074151 A074152
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KEYWORD
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nonn,easy
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AUTHOR
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Amarnath Murthy, Aug 28 2002
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EXTENSIONS
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More terms from Franklin T. Adams-Watters, Jul 17 2006
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STATUS
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approved
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