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A027441 (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

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

Eric Weisstein's World of Mathematics, Magic Constant

Eric Weisstein's World of Mathematics, Magic Cube

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

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 *)

PROG

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

(PARI) a(n)=([0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1; 1, -5, 10, -10, 5]^n*[0; 1; 9; 42; 130])[1, 1] \\ Charles R Greathouse IV, Jul 28 2015

CROSSREFS

Subsequence of A057590.

Cf. A002061, A139562, A179268.

Sequence in context: A062783 A172464 A269053 * A000971 A061927 A051923

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 10 12:02 EST 2016. Contains 279002 sequences.