A074149 Sum of terms in each group in A074147.

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

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

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

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
(Python)
def A074149(n): return (n*(n**2-(n&1))>>1)+n # Chai Wah Wu, Aug 30 2022

Crossrefs

Cf. A000035, 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