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A048396 Sums of consecutive noncubes. 5
0, 27, 315, 1638, 5670, 15345, 35217, 71820, 134028, 233415, 384615, 605682, 918450, 1348893, 1927485, 2689560, 3675672, 4931955, 6510483, 8469630, 10874430, 13796937, 17316585, 21520548, 26504100, 32370975, 39233727, 47214090, 56443338, 67062645, 79223445 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Relation with triangular numbers: a(n) = 3*((n^3+1) + ((n+1)^3-1)) * A000217(n). Example: a(3) = 3*(first term + last term)*A000217(3) = 3*(28+63)*6 = 1638.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

FORMULA

a(n) = ( 6n^5 + 15n^4 + 18n^3 + 12n^2 + 3n ) / 2.

G.f.: 9*x*(1+x)*(3+14*x+3*x^2)/(1-x)^6. - Colin Barker, Mar 15 2012

a(n) = 6*a(n-1)-15*a(n-2)+20*a(n-3)-15*a(n-4)+6*a(n-5)-a(n-6). - Wesley Ivan Hurt, Apr 10 2015

EXAMPLE

Between 3^3 and 4^3 we have: 28 + 29 + ... + 62 + 63 = 1638 = a(3).

MAPLE

A048396:=n->(6*n^5+15*n^4+18*n^3+12*n^2+3*n)/2: seq(A048396(n), n=0..50); # Wesley Ivan Hurt, Apr 10 2015

MATHEMATICA

Table[Total[Range[n^3+1, (n+1)^3-1]], {n, 0, 30}] (* Harvey P. Dale, Jan 08 2011 *)

PROG

(MAGMA) [(6*n^5+15*n^4+18*n^3+12*n^2+3*n)/2 : n in [0..50]]; // Wesley Ivan Hurt, Apr 10 2015

(PARI) a(n)=(6*n^5+15*n^4+18*n^3+12*n^2+3*n)/2 \\ Charles R Greathouse IV, Oct 07 2015

CROSSREFS

Cf. A000217, A048395, A048397.

Sequence in context: A274832 A125415 A119295 * A061181 A231911 A182130

Adjacent sequences:  A048393 A048394 A048395 * A048397 A048398 A048399

KEYWORD

nonn,easy,nice

AUTHOR

Patrick De Geest, Mar 15 1999

STATUS

approved

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Last modified October 18 07:42 EDT 2019. Contains 328146 sequences. (Running on oeis4.)