A048396 Sums of consecutive noncubes.

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

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 *)
LinearRecurrence[{6, -15, 20, -15, 6, -1}, {0, 27, 315, 1638, 5670, 15345}, 40] (* Harvey P. Dale, Nov 02 2024 *)

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
(Python)
def A048396(n): return n*(n*(n*(n*(6*n + 15) + 18) + 12) + 3)>>1 # Chai Wah Wu, Sep 04 2024

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