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A027441 a(n) = (n^4 + n)/2, (Row sums of an n X n X n magic cube, when it exists). 80
0, 1, 9, 42, 130, 315, 651, 1204, 2052, 3285, 5005, 7326, 10374, 14287, 19215, 25320, 32776, 41769, 52497, 65170, 80010, 97251, 117139, 139932, 165900, 195325, 228501, 265734, 307342, 353655, 405015, 461776, 524304, 592977, 668185, 750330, 839826, 937099 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Starting with offset 1 = binomial transform of (1, 8, 25, 30, 12, 0, 0, 0,...). - Gary W. Adamson, May 20 2009

a(n) = sum(k: n<=k<=n^2); for n>0: a(n) = A037270(n) - A000217(n-1). - Reinhard Zumkeller, Jul 06 2010

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..680

Eric Weisstein's World of Mathematics, Magic Constant

Eric Weisstein's World of Mathematics, Magic Cube

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

FORMULA

O.g.f.: x*(1+4*x+7*x^2)/(1-x)^5. - R. J. Mathar, Feb 13 2008

a(n) = 5*a(n-1)-10*a(n-2)+10*a(n-3)-5*a(n-4)+a(n-5). - Wesley Ivan Hurt, Aug 13 2014

a(n) = ( sum_{i=1..n^3} i ) / n^2, for n > 0. - Wesley Ivan Hurt, Aug 13 2014

a(n) = A002061(n)*A000217(n). - Anton Zakharov, Dec 16 2016

a(n) = (n+1)*(a(n-1)/(n-1) + n*(n-1)), a(0)=0, a(1)=1. - Vladimir Kruchinin, Oct 10 2018

MAPLE

A027441:=n->(n^4+n)/2: seq(A027441(n), n=0..30); # Wesley Ivan Hurt, Aug 13 2014

MATHEMATICA

Table[(n^4 + n)/2, {n, 0, 30}] (* Wesley Ivan Hurt, Aug 13 2014 *)

LinearRecurrence[{5, -10, 10, -5, 1}, {0, 1, 9, 42, 130}, 40] (* Harvey P. Dale, Apr 09 2018 *)

PROG

(MAGMA) [(n^4+n)/2: n in [0..50]]; // Vincenzo Librandi, Apr 29 2011

(PARI) a(n)=(n^4 + n)/2 \\ Charles R Greathouse IV, Jul 28 2015

CROSSREFS

Subsequence of A057590.

Cf. A002061, A139562, A179268.

Sequence in context: A062783 A172464 A269053 * A000971 A061927 A292481

Adjacent sequences:  A027438 A027439 A027440 * A027442 A027443 A027444

KEYWORD

nonn,easy

AUTHOR

Eric W. Weisstein

EXTENSIONS

More terms from Wesley Ivan Hurt, Aug 13 2014

STATUS

approved

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Last modified December 12 22:06 EST 2019. Contains 329963 sequences. (Running on oeis4.)